LMFDB - Space of modular forms of level 7410, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 7410 = 2 \cdot 3 \cdot 5 \cdot 13 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7410.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 56 $
Sturm bound:			$3360$
Trace bound:			$13$
Distinguishing $T_p$:			$7$, $11$, $17$, $23$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(7410))$.

	Total	New	Old
Modular forms	1696	143	1553
Cusp forms	1665	143	1522
Eisenstein series	31	0	31

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$2$	$3$	$5$	$13$	$19$	Fricke	Total			Cusp			Eisenstein
$2$	$3$	$5$	$13$	$19$	Fricke	All	New	Old	All	New	Old	All	New	Old
$+$	$+$	$+$	$+$	$+$	$+$	$43$	$6$	$37$	$43$	$6$	$37$	$0$	$0$	$0$
$+$	$+$	$+$	$+$	$-$	$-$	$61$	$2$	$59$	$60$	$2$	$58$	$1$	$0$	$1$
$+$	$+$	$+$	$-$	$+$	$-$	$57$	$4$	$53$	$56$	$4$	$52$	$1$	$0$	$1$
$+$	$+$	$+$	$-$	$-$	$+$	$51$	$6$	$45$	$50$	$6$	$44$	$1$	$0$	$1$
$+$	$+$	$-$	$+$	$+$	$-$	$57$	$5$	$52$	$56$	$5$	$51$	$1$	$0$	$1$
$+$	$+$	$-$	$+$	$-$	$+$	$51$	$5$	$46$	$50$	$5$	$45$	$1$	$0$	$1$
$+$	$+$	$-$	$-$	$+$	$+$	$53$	$4$	$49$	$52$	$4$	$48$	$1$	$0$	$1$
$+$	$+$	$-$	$-$	$-$	$-$	$51$	$4$	$47$	$50$	$4$	$46$	$1$	$0$	$1$
$+$	$-$	$+$	$+$	$+$	$-$	$50$	$4$	$46$	$49$	$4$	$45$	$1$	$0$	$1$
$+$	$-$	$+$	$+$	$-$	$+$	$56$	$5$	$51$	$55$	$5$	$50$	$1$	$0$	$1$
$+$	$-$	$+$	$-$	$+$	$+$	$54$	$3$	$51$	$53$	$3$	$50$	$1$	$0$	$1$
$+$	$-$	$+$	$-$	$-$	$-$	$52$	$6$	$46$	$51$	$6$	$45$	$1$	$0$	$1$
$+$	$-$	$-$	$+$	$+$	$+$	$55$	$3$	$52$	$54$	$3$	$51$	$1$	$0$	$1$
$+$	$-$	$-$	$+$	$-$	$-$	$51$	$6$	$45$	$50$	$6$	$44$	$1$	$0$	$1$
$+$	$-$	$-$	$-$	$+$	$-$	$55$	$7$	$48$	$54$	$7$	$47$	$1$	$0$	$1$
$+$	$-$	$-$	$-$	$-$	$+$	$51$	$2$	$49$	$50$	$2$	$48$	$1$	$0$	$1$
$-$	$+$	$+$	$+$	$+$	$-$	$50$	$4$	$46$	$49$	$4$	$45$	$1$	$0$	$1$
$-$	$+$	$+$	$+$	$-$	$+$	$56$	$5$	$51$	$55$	$5$	$50$	$1$	$0$	$1$
$-$	$+$	$+$	$-$	$+$	$+$	$52$	$5$	$47$	$51$	$5$	$46$	$1$	$0$	$1$
$-$	$+$	$+$	$-$	$-$	$-$	$54$	$4$	$50$	$53$	$4$	$49$	$1$	$0$	$1$
$-$	$+$	$-$	$+$	$+$	$+$	$59$	$4$	$55$	$58$	$4$	$54$	$1$	$0$	$1$
$-$	$+$	$-$	$+$	$-$	$-$	$47$	$5$	$42$	$46$	$5$	$41$	$1$	$0$	$1$
$-$	$+$	$-$	$-$	$+$	$-$	$53$	$6$	$47$	$52$	$6$	$46$	$1$	$0$	$1$
$-$	$+$	$-$	$-$	$-$	$+$	$53$	$3$	$50$	$52$	$3$	$49$	$1$	$0$	$1$
$-$	$-$	$+$	$+$	$+$	$+$	$50$	$4$	$46$	$49$	$4$	$45$	$1$	$0$	$1$
$-$	$-$	$+$	$+$	$-$	$-$	$54$	$6$	$48$	$53$	$6$	$47$	$1$	$0$	$1$
$-$	$-$	$+$	$-$	$+$	$-$	$52$	$6$	$46$	$51$	$6$	$45$	$1$	$0$	$1$
$-$	$-$	$+$	$-$	$-$	$+$	$56$	$2$	$54$	$55$	$2$	$53$	$1$	$0$	$1$
$-$	$-$	$-$	$+$	$+$	$-$	$60$	$6$	$54$	$59$	$6$	$53$	$1$	$0$	$1$
$-$	$-$	$-$	$+$	$-$	$+$	$48$	$2$	$46$	$47$	$2$	$45$	$1$	$0$	$1$
$-$	$-$	$-$	$-$	$+$	$+$	$48$	$1$	$47$	$47$	$1$	$46$	$1$	$0$	$1$
$-$	$-$	$-$	$-$	$-$	$-$	$56$	$8$	$48$	$55$	$8$	$47$	$1$	$0$	$1$
Plus space					$+$	$836$	$60$	$776$	$821$	$60$	$761$	$15$	$0$	$15$
Minus space					$-$	$860$	$83$	$777$	$844$	$83$	$761$	$16$	$0$	$16$

Trace form

$ 143 q - q^{2} - q^{3} + 143 q^{4} - q^{5} - q^{6} - 8 q^{7} - q^{8} + 143 q^{9} - q^{10} - 12 q^{11} - q^{12} - q^{13} - 8 q^{14} - q^{15} + 143 q^{16} - 18 q^{17} - q^{18} - q^{19} - q^{20}+ \cdots - 12 q^{99}+O(q^{100}) $

143 * q - q^2 - q^3 + 143 * q^4 - q^5 - q^6 - 8 * q^7 - q^8 + 143 * q^9 - q^10 - 12 * q^11 - q^12 - q^13 - 8 * q^14 - q^15 + 143 * q^16 - 18 * q^17 - q^18 - q^19 - q^20 - 8 * q^21 - 12 * q^22 - 24 * q^23 - q^24 + 143 * q^25 - q^26 - q^27 - 8 * q^28 + 2 * q^29 - q^30 + 32 * q^31 - q^32 + 20 * q^33 - 18 * q^34 + 24 * q^35 + 143 * q^36 - 6 * q^37 - q^38 - q^39 - q^40 + 22 * q^41 - 8 * q^42 + 20 * q^43 - 12 * q^44 - q^45 - 24 * q^46 + 48 * q^47 - q^48 + 199 * q^49 - q^50 + 30 * q^51 - q^52 + 42 * q^53 - q^54 + 4 * q^55 - 8 * q^56 + 7 * q^57 + 2 * q^58 + 68 * q^59 - q^60 + 34 * q^61 - 8 * q^63 + 143 * q^64 - q^65 + 4 * q^66 + 60 * q^67 - 18 * q^68 + 24 * q^69 - 8 * q^70 - 8 * q^71 - q^72 + 38 * q^73 + 58 * q^74 - q^75 - q^76 + 32 * q^77 - q^78 - 32 * q^79 - q^80 + 143 * q^81 + 38 * q^82 - 20 * q^83 - 8 * q^84 + 30 * q^85 - 12 * q^86 + 34 * q^87 - 12 * q^88 + 70 * q^89 - q^90 + 8 * q^91 - 24 * q^92 + 48 * q^94 - q^95 - q^96 - 2 * q^97 + 7 * q^98 - 12 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(7410))$ into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				A-L signs					Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	5	13	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
7410.2.a.a	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.a	$1$	$0$	$-1$	$-1$	$-1$	$0$	$+$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots$
7410.2.a.b	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.b	$1$	$0$	$-1$	$-1$	$-1$	$0$	$+$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots$
7410.2.a.c	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.c	$1$	$1$	$-1$	$-1$	$-1$	$3$	$+$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+3q^{7}+\cdots$
7410.2.a.d	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.d	$1$	$0$	$-1$	$-1$	$1$	$-5$	$+$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-5q^{7}+\cdots$
7410.2.a.e	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.e	$1$	$0$	$-1$	$-1$	$1$	$-2$	$+$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots$
7410.2.a.f	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.f	$1$	$0$	$-1$	$-1$	$1$	$0$	$+$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots$
7410.2.a.g	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.g	$1$	$0$	$-1$	$-1$	$1$	$4$	$+$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots$
7410.2.a.h	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.h	$1$	$0$	$-1$	$-1$	$1$	$4$	$+$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots$
7410.2.a.i	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.i	$1$	$0$	$-1$	$1$	$-1$	$0$	$+$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
7410.2.a.j	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.j	$1$	$1$	$-1$	$1$	$-1$	$1$	$+$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
7410.2.a.k	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.k	$1$	$0$	$-1$	$1$	$-1$	$4$	$+$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+4q^{7}+\cdots$
7410.2.a.l	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.l	$1$	$1$	$-1$	$1$	$1$	$0$	$+$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots$
7410.2.a.m	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.m	$1$	$0$	$-1$	$1$	$1$	$2$	$+$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots$
7410.2.a.n	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.n	$1$	$0$	$1$	$-1$	$1$	$-4$	$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots$
7410.2.a.o	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.o	$1$	$0$	$1$	$-1$	$1$	$-3$	$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-3q^{7}+\cdots$
7410.2.a.p	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.p	$1$	$1$	$1$	$-1$	$1$	$0$	$-$	$+$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
7410.2.a.q	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.q	$1$	$0$	$1$	$-1$	$1$	$0$	$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
7410.2.a.r	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.r	$1$	$0$	$1$	$-1$	$1$	$2$	$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots$
7410.2.a.s	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.s	$1$	$1$	$1$	$1$	$-1$	$-4$	$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-4q^{7}+\cdots$
7410.2.a.t	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.t	$1$	$1$	$1$	$1$	$-1$	$-1$	$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
7410.2.a.u	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.u	$1$	$1$	$1$	$1$	$-1$	$0$	$-$	$-$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
7410.2.a.v	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓	✓	✓	7410.2.a.v	$1$	$1$	$1$	$1$	$1$	$-2$	$-$	$-$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots$
7410.2.a.w	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.w	$1$	$0$	$1$	$1$	$1$	$-1$	$-$	$-$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots$
7410.2.a.x	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.x	$1$	$0$	$1$	$1$	$1$	$4$	$-$	$-$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots$
7410.2.a.y	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{17}) $	None	✓	✓			7410.2.a.y	$1$	$0$	$-2$	$-2$	$-2$	$0$	$+$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots$
7410.2.a.z	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{2}) $	None	✓	✓			7410.2.a.z	$1$	$0$	$-2$	$-2$	$-2$	$0$	$+$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+3\beta q^{7}+\cdots$
7410.2.a.ba	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{2}) $	None	✓	✓	✓		7410.2.a.ba	$1$	$1$	$-2$	$2$	$-2$	$-4$	$+$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(-2+\cdots)q^{7}+\cdots$
7410.2.a.bb	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{97}) $	None	✓	✓	✓		7410.2.a.bb	$1$	$0$	$-2$	$2$	$-2$	$0$	$+$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
7410.2.a.bc	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{5}) $	None	✓	✓	✓		7410.2.a.bc	$1$	$1$	$-2$	$2$	$2$	$-2$	$+$	$-$	$-$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
7410.2.a.bd	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{3}) $	None	✓	✓	✓	✓	7410.2.a.bd	$1$	$1$	$-2$	$2$	$2$	$-2$	$+$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
7410.2.a.be	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{2}) $	None	✓	✓			7410.2.a.be	$1$	$0$	$2$	$-2$	$-2$	$0$	$-$	$+$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+3\beta q^{7}+\cdots$
7410.2.a.bf	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{17}) $	None	✓	✓			7410.2.a.bf	$1$	$0$	$2$	$-2$	$-2$	$0$	$-$	$+$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
7410.2.a.bg	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{5}) $	None	✓	✓			7410.2.a.bg	$1$	$1$	$2$	$-2$	$-2$	$4$	$-$	$+$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots$
7410.2.a.bh	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{5}) $	None	✓	✓	✓		7410.2.a.bh	$1$	$1$	$2$	$-2$	$2$	$-2$	$-$	$+$	$-$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
7410.2.a.bi	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{17}) $	None	✓	✓			7410.2.a.bi	$1$	$0$	$2$	$-2$	$2$	$1$	$-$	$+$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+\beta q^{7}+\cdots$
7410.2.a.bj	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{57}) $	None	✓	✓	✓		7410.2.a.bj	$1$	$0$	$2$	$-2$	$2$	$8$	$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+4q^{7}+\cdots$
7410.2.a.bk	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{2}) $	None	✓	✓	✓	✓	7410.2.a.bk	$1$	$1$	$2$	$2$	$2$	$-4$	$-$	$-$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots$
7410.2.a.bl	$7410$	$2$	7410.a	1.a	$1$	$3$	$3$	$59.169$	3.3.837.1	None	✓	✓	✓		7410.2.a.bl	$1$	$1$	$3$	$-3$	$-3$	$-3$	$-$	$+$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
7410.2.a.bm	$7410$	$2$	7410.a	1.a	$1$	$3$	$3$	$59.169$	3.3.3580.1	None	✓	✓	✓		7410.2.a.bm	$1$	$0$	$3$	$-3$	$3$	$-2$	$-$	$+$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
7410.2.a.bn	$7410$	$2$	7410.a	1.a	$1$	$3$	$3$	$59.169$	3.3.568.1	None	✓	✓	✓		7410.2.a.bn	$1$	$1$	$3$	$3$	$-3$	$-5$	$-$	$-$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots$
7410.2.a.bo	$7410$	$2$	7410.a	1.a	$1$	$4$	$4$	$59.169$	4.4.85688.1	None	✓	✓	✓	✓	7410.2.a.bo	$1$	$0$	$-4$	$-4$	$4$	$-1$	$+$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-\beta _{1}q^{7}+\cdots$
7410.2.a.bp	$7410$	$2$	7410.a	1.a	$1$	$4$	$4$	$59.169$	4.4.11344.1	None	✓	✓	✓	✓	7410.2.a.bp	$1$	$1$	$-4$	$-4$	$4$	$0$	$+$	$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+\beta _{1}q^{7}+\cdots$
7410.2.a.bq	$7410$	$2$	7410.a	1.a	$1$	$4$	$4$	$59.169$	4.4.15188.1	None	✓	✓	✓	✓	7410.2.a.bq	$1$	$0$	$4$	$-4$	$-4$	$-2$	$-$	$+$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+\beta _{3}q^{7}+\cdots$
7410.2.a.br	$7410$	$2$	7410.a	1.a	$1$	$4$	$4$	$59.169$	$\Q(\zeta_{16})^+$	None	✓	✓	✓	✓	7410.2.a.br	$1$	$1$	$4$	$-4$	$4$	$0$	$-$	$+$	$-$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-\beta _{2}+\cdots)q^{7}+\cdots$
7410.2.a.bs	$7410$	$2$	7410.a	1.a	$1$	$4$	$4$	$59.169$	4.4.324176.1	None	✓	✓	✓		7410.2.a.bs	$1$	$0$	$4$	$4$	$4$	$0$	$-$	$-$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-\beta _{1}q^{7}+\cdots$
7410.2.a.bt	$7410$	$2$	7410.a	1.a	$1$	$5$	$5$	$59.169$	5.5.4894544.1	None	✓	✓	✓		7410.2.a.bt	$1$	$1$	$-5$	$-5$	$-5$	$-2$	$+$	$+$	$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+\beta _{4}q^{7}+\cdots$
7410.2.a.bu	$7410$	$2$	7410.a	1.a	$1$	$5$	$5$	$59.169$	5.5.394064.1	None	✓	✓	✓	✓	7410.2.a.bu	$1$	$1$	$-5$	$-5$	$5$	$4$	$+$	$+$	$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
7410.2.a.bv	$7410$	$2$	7410.a	1.a	$1$	$5$	$5$	$59.169$	5.5.998068.1	None	✓	✓	✓	✓	7410.2.a.bv	$1$	$1$	$-5$	$5$	$-5$	$-9$	$+$	$-$	$+$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(-2+\cdots)q^{7}+\cdots$
7410.2.a.bw	$7410$	$2$	7410.a	1.a	$1$	$5$	$5$	$59.169$	5.5.9733193.1	None	✓	✓	✓		7410.2.a.bw	$1$	$0$	$-5$	$5$	$5$	$1$	$+$	$-$	$-$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+\beta _{1}q^{7}+\cdots$
7410.2.a.bx	$7410$	$2$	7410.a	1.a	$1$	$5$	$5$	$59.169$	5.5.1493248.1	None	✓	✓	✓	✓	7410.2.a.bx	$1$	$1$	$5$	$-5$	$-5$	$1$	$-$	$+$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+\beta _{2}q^{7}+\cdots$
7410.2.a.by	$7410$	$2$	7410.a	1.a	$1$	$6$	$6$	$59.169$	6.6.810777168.1	None	✓	✓	✓	✓	7410.2.a.by	$1$	$1$	$-6$	$-6$	$-6$	$-5$	$+$	$+$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots$
7410.2.a.bz	$7410$	$2$	7410.a	1.a	$1$	$6$	$6$	$59.169$	6.6.360407552.1	None	✓	✓	✓	✓	7410.2.a.bz	$1$	$0$	$-6$	$6$	$-6$	$4$	$+$	$-$	$+$	$-$	$-$	$-$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(1-\beta _{5})q^{7}+\cdots$
7410.2.a.ca	$7410$	$2$	7410.a	1.a	$1$	$6$	$6$	$59.169$	6.6.997608784.1	None	✓	✓	✓	✓	7410.2.a.ca	$1$	$0$	$6$	$6$	$-6$	$0$	$-$	$-$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-\beta _{4}q^{7}+\cdots$
7410.2.a.cb	$7410$	$2$	7410.a	1.a	$1$	$6$	$6$	$59.169$	6.6.967258064.1	None	✓	✓	✓	✓	7410.2.a.cb	$1$	$0$	$6$	$6$	$-6$	$2$	$-$	$-$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+\beta _{1}q^{7}+\cdots$
7410.2.a.cc	$7410$	$2$	7410.a	1.a	$1$	$7$	$7$	$59.169$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓	✓	7410.2.a.cc	$1$	$0$	$-7$	$7$	$7$	$5$	$+$	$-$	$-$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
7410.2.a.cd	$7410$	$2$	7410.a	1.a	$1$	$8$	$8$	$59.169$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓	✓	7410.2.a.cd	$1$	$0$	$8$	$8$	$8$	$3$	$-$	$-$	$-$	$-$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+\beta _{1}q^{7}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(7410))$ into lower level spaces

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 7410 = 2 \cdot 3 \cdot 5 \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7410.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 56 \)
Sturm bound:			\(3360\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\), \(11\), \(17\), \(23\)

\(2\)	\(3\)	\(5\)	\(13\)	\(19\)	Fricke	Total			Cusp			Eisenstein
\(2\)	\(3\)	\(5\)	\(13\)	\(19\)	Fricke	All	New	Old	All	New	Old	All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(43\)	\(6\)	\(37\)	\(43\)	\(6\)	\(37\)	\(0\)	\(0\)	\(0\)
\(+\)	\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(61\)	\(2\)	\(59\)	\(60\)	\(2\)	\(58\)	\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(57\)	\(4\)	\(53\)	\(56\)	\(4\)	\(52\)	\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(51\)	\(6\)	\(45\)	\(50\)	\(6\)	\(44\)	\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(57\)	\(5\)	\(52\)	\(56\)	\(5\)	\(51\)	\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(51\)	\(5\)	\(46\)	\(50\)	\(5\)	\(45\)	\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(53\)	\(4\)	\(49\)	\(52\)	\(4\)	\(48\)	\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(51\)	\(4\)	\(47\)	\(50\)	\(4\)	\(46\)	\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(50\)	\(4\)	\(46\)	\(49\)	\(4\)	\(45\)	\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(56\)	\(5\)	\(51\)	\(55\)	\(5\)	\(50\)	\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(54\)	\(3\)	\(51\)	\(53\)	\(3\)	\(50\)	\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(52\)	\(6\)	\(46\)	\(51\)	\(6\)	\(45\)	\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(55\)	\(3\)	\(52\)	\(54\)	\(3\)	\(51\)	\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(51\)	\(6\)	\(45\)	\(50\)	\(6\)	\(44\)	\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(55\)	\(7\)	\(48\)	\(54\)	\(7\)	\(47\)	\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(51\)	\(2\)	\(49\)	\(50\)	\(2\)	\(48\)	\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(+\)	\(+\)	\(-\)	\(50\)	\(4\)	\(46\)	\(49\)	\(4\)	\(45\)	\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(+\)	\(56\)	\(5\)	\(51\)	\(55\)	\(5\)	\(50\)	\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(+\)	\(52\)	\(5\)	\(47\)	\(51\)	\(5\)	\(46\)	\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)	\(-\)	\(-\)	\(54\)	\(4\)	\(50\)	\(53\)	\(4\)	\(49\)	\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(+\)	\(59\)	\(4\)	\(55\)	\(58\)	\(4\)	\(54\)	\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)	\(-\)	\(-\)	\(47\)	\(5\)	\(42\)	\(46\)	\(5\)	\(41\)	\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(-\)	\(+\)	\(-\)	\(53\)	\(6\)	\(47\)	\(52\)	\(6\)	\(46\)	\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(+\)	\(53\)	\(3\)	\(50\)	\(52\)	\(3\)	\(49\)	\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(+\)	\(50\)	\(4\)	\(46\)	\(49\)	\(4\)	\(45\)	\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)	\(-\)	\(-\)	\(54\)	\(6\)	\(48\)	\(53\)	\(6\)	\(47\)	\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(-\)	\(+\)	\(-\)	\(52\)	\(6\)	\(46\)	\(51\)	\(6\)	\(45\)	\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(+\)	\(56\)	\(2\)	\(54\)	\(55\)	\(2\)	\(53\)	\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(+\)	\(+\)	\(-\)	\(60\)	\(6\)	\(54\)	\(59\)	\(6\)	\(53\)	\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(+\)	\(48\)	\(2\)	\(46\)	\(47\)	\(2\)	\(45\)	\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(+\)	\(48\)	\(1\)	\(47\)	\(47\)	\(1\)	\(46\)	\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)	\(-\)	\(-\)	\(56\)	\(8\)	\(48\)	\(55\)	\(8\)	\(47\)	\(1\)	\(0\)	\(1\)
Plus space					\(+\)	\(836\)	\(60\)	\(776\)	\(821\)	\(60\)	\(761\)	\(15\)	\(0\)	\(15\)
Minus space					\(-\)	\(860\)	\(83\)	\(777\)	\(844\)	\(83\)	\(761\)	\(16\)	\(0\)	\(16\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7410))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7410))\) into lower level spaces

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	7410.2.a

Level	$7410$
Weight	$2$
Character orbit	7410.a
Rep. character	$\chi_{7410}(1,\cdot)$
Character field	$\Q$
Dimension	$143$
Newform subspaces	$56$
Sturm bound	$3360$
Trace bound	$13$