LMFDB - Space of modular forms of level 8112, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 8112 = 2^{4} \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8112.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 75 $
Sturm bound:			$2912$
Trace bound:			$17$
Distinguishing $T_p$:			$5$, $7$, $11$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(8112))$.

	Total	New	Old
Modular forms	1540	155	1385
Cusp forms	1373	155	1218
Eisenstein series	167	0	167

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

$2$	$3$	$13$	Fricke	Total			Cusp			Eisenstein
$2$	$3$	$13$	Fricke	All	New	Old	All	New	Old	All	New	Old
$+$	$+$	$+$	$+$	$189$	$18$	$171$	$169$	$18$	$151$	$20$	$0$	$20$
$+$	$+$	$-$	$-$	$195$	$21$	$174$	$174$	$21$	$153$	$21$	$0$	$21$
$+$	$-$	$+$	$-$	$196$	$23$	$173$	$175$	$23$	$152$	$21$	$0$	$21$
$+$	$-$	$-$	$+$	$190$	$15$	$175$	$169$	$15$	$154$	$21$	$0$	$21$
$-$	$+$	$+$	$-$	$196$	$18$	$178$	$175$	$18$	$157$	$21$	$0$	$21$
$-$	$+$	$-$	$+$	$190$	$21$	$169$	$169$	$21$	$148$	$21$	$0$	$21$
$-$	$-$	$+$	$+$	$189$	$18$	$171$	$168$	$18$	$150$	$21$	$0$	$21$
$-$	$-$	$-$	$-$	$195$	$21$	$174$	$174$	$21$	$153$	$21$	$0$	$21$
Plus space			$+$	$758$	$72$	$686$	$675$	$72$	$603$	$83$	$0$	$83$
Minus space			$-$	$782$	$83$	$699$	$698$	$83$	$615$	$84$	$0$	$84$

Trace form

$ 155 q - q^{3} + 2 q^{5} - 4 q^{7} + 155 q^{9} - 4 q^{11} - 2 q^{15} - 2 q^{17} + 8 q^{23} + 149 q^{25} - q^{27} + 10 q^{29} - 12 q^{31} - 4 q^{33} + 10 q^{37} + 6 q^{41} - 4 q^{43} + 2 q^{45} - 24 q^{47}+ \cdots - 4 q^{99}+O(q^{100}) $

155 * q - q^3 + 2 * q^5 - 4 * q^7 + 155 * q^9 - 4 * q^11 - 2 * q^15 - 2 * q^17 + 8 * q^23 + 149 * q^25 - q^27 + 10 * q^29 - 12 * q^31 - 4 * q^33 + 10 * q^37 + 6 * q^41 - 4 * q^43 + 2 * q^45 - 24 * q^47 + 155 * q^49 - 10 * q^51 + 18 * q^53 + 16 * q^55 - 4 * q^57 + 4 * q^59 + 18 * q^61 - 4 * q^63 - 24 * q^67 + 8 * q^69 + 24 * q^71 - 18 * q^73 + q^75 + 16 * q^77 - 24 * q^79 + 155 * q^81 + 44 * q^83 + 4 * q^85 - 6 * q^87 + 6 * q^89 - 8 * q^93 - 16 * q^95 + 6 * q^97 - 4 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(8112))$ 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	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
8112.2.a.a	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				312.2.c.c	$1$	$0$	$0$	$-1$	$-4$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots$
8112.2.a.b	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				312.2.q.a	$1$	$1$	$0$	$-1$	$-3$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}+q^{9}+3q^{15}-q^{17}+\cdots$
8112.2.a.c	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				78.2.e.a	$1$	$0$	$0$	$-1$	$-3$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}+2q^{7}+q^{9}+6q^{11}+\cdots$
8112.2.a.d	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				156.2.b.b	$1$	$1$	$0$	$-1$	$-2$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-4q^{7}+q^{9}+6q^{11}+\cdots$
8112.2.a.e	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				312.2.c.b	$1$	$2$	$0$	$-1$	$-2$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots$
8112.2.a.f	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				312.2.a.f	$1$	$1$	$0$	$-1$	$-2$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{9}+2q^{15}+2q^{17}+\cdots$
8112.2.a.g	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				78.2.b.a	$1$	$1$	$0$	$-1$	$-2$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+2q^{7}+q^{9}+2q^{15}+\cdots$
8112.2.a.h	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				312.2.a.e	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}+6q^{11}+2q^{17}-4q^{23}+\cdots$
8112.2.a.i	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				156.2.a.b	$1$	$0$	$0$	$-1$	$0$	$2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}-6q^{17}+2q^{19}+\cdots$
8112.2.a.j	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				78.2.b.a	$1$	$1$	$0$	$-1$	$2$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-2q^{7}+q^{9}-2q^{15}+\cdots$
8112.2.a.k	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				312.2.c.b	$1$	$0$	$0$	$-1$	$2$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots$
8112.2.a.l	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				156.2.b.b	$1$	$1$	$0$	$-1$	$2$	$4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+4q^{7}+q^{9}-6q^{11}+\cdots$
8112.2.a.m	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				78.2.e.a	$1$	$0$	$0$	$-1$	$3$	$-2$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}-2q^{7}+q^{9}-6q^{11}+\cdots$
8112.2.a.n	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				312.2.q.a	$1$	$1$	$0$	$-1$	$3$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}+q^{9}-3q^{15}-q^{17}+\cdots$
8112.2.a.o	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				312.2.a.d	$1$	$1$	$0$	$-1$	$4$	$-4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{5}-4q^{7}+q^{9}-2q^{11}+\cdots$
8112.2.a.p	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				312.2.c.c	$1$	$0$	$0$	$-1$	$4$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots$
8112.2.a.q	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				312.2.a.c	$1$	$0$	$0$	$1$	$-4$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}+q^{9}-2q^{11}-4q^{15}+\cdots$
8112.2.a.r	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				312.2.q.c	$1$	$0$	$0$	$1$	$-3$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots$
8112.2.a.s	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				39.2.a.a	$1$	$1$	$0$	$1$	$-2$	$-4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots$
8112.2.a.t	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				312.2.q.b	$1$	$0$	$0$	$1$	$-2$	$-1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}-q^{7}+q^{9}+6q^{11}-2q^{15}+\cdots$
8112.2.a.u	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				156.2.i.a	$1$	$1$	$0$	$1$	$-2$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{7}+q^{9}+2q^{11}-2q^{15}+\cdots$
8112.2.a.v	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				78.2.a.a	$1$	$1$	$0$	$1$	$-2$	$4$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots$
8112.2.a.w	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				39.2.e.a	$1$	$1$	$0$	$1$	$-1$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{7}+q^{9}+2q^{11}-q^{15}+\cdots$
8112.2.a.x	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				78.2.e.b	$1$	$1$	$0$	$1$	$-1$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+2q^{7}+q^{9}-2q^{11}-q^{15}+\cdots$
8112.2.a.y	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				312.2.a.b	$1$	$0$	$0$	$1$	$0$	$-4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{7}+q^{9}-2q^{11}-6q^{17}+\cdots$
8112.2.a.z	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				312.2.c.a	$1$	$1$	$0$	$1$	$0$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}+q^{9}-2q^{11}-2q^{17}+\cdots$
8112.2.a.ba	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				312.2.c.a	$1$	$1$	$0$	$1$	$0$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}+q^{9}+2q^{11}-2q^{17}+\cdots$
8112.2.a.bb	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				78.2.e.b	$1$	$1$	$0$	$1$	$1$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{7}+q^{9}+2q^{11}+q^{15}+\cdots$
8112.2.a.bc	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				39.2.e.a	$1$	$1$	$0$	$1$	$1$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+2q^{7}+q^{9}-2q^{11}+q^{15}+\cdots$
8112.2.a.bd	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				156.2.i.a	$1$	$1$	$0$	$1$	$2$	$-1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-q^{7}+q^{9}-2q^{11}+2q^{15}+\cdots$
8112.2.a.be	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				24.2.a.a	$1$	$0$	$0$	$1$	$2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{9}+4q^{11}+2q^{15}+\cdots$
8112.2.a.bf	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				312.2.q.b	$1$	$0$	$0$	$1$	$2$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{7}+q^{9}-6q^{11}+2q^{15}+\cdots$
8112.2.a.bg	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				312.2.a.a	$1$	$0$	$0$	$1$	$2$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+4q^{7}+q^{9}+2q^{15}+\cdots$
8112.2.a.bh	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				312.2.q.c	$1$	$0$	$0$	$1$	$3$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots$
8112.2.a.bi	$8112$	$2$	8112.a	1.a	$1$	$1$	$1$	$64.775$	$\Q$	None	✓				156.2.a.a	$1$	$1$	$0$	$1$	$4$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots$
8112.2.a.bj	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	$\Q(\sqrt{3}) $	None	✓				78.2.i.a	$1$	$1$	$0$	$-2$	$-4$	$-2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-2+\beta )q^{5}+(-1+\beta )q^{7}+\cdots$
8112.2.a.bk	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	$\Q(\sqrt{17}) $	None	✓				39.2.e.b	$1$	$0$	$0$	$-2$	$-3$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta )q^{5}+(2-\beta )q^{7}+q^{9}+\cdots$
8112.2.a.bl	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	$\Q(\sqrt{13}) $	None	✓				312.2.q.d	$1$	$1$	$0$	$-2$	$-2$	$-2$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+(-1+\beta )q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots$
8112.2.a.bm	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	$\Q(\sqrt{2}) $	None	✓				39.2.a.b	$1$	$0$	$0$	$-2$	$0$	$0$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}+\beta q^{7}+q^{9}-2q^{11}+\cdots$
8112.2.a.bn	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	$\Q(\sqrt{13}) $	None	✓				312.2.q.d	$1$	$1$	$0$	$-2$	$2$	$2$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
8112.2.a.bo	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	$\Q(\sqrt{17}) $	None	✓				39.2.e.b	$1$	$0$	$0$	$-2$	$3$	$-3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta )q^{5}+(-2+\beta )q^{7}+q^{9}+\cdots$
8112.2.a.bp	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	$\Q(\sqrt{3}) $	None	✓				78.2.i.a	$1$	$1$	$0$	$-2$	$4$	$2$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(2+\beta )q^{5}+(1+\beta )q^{7}+q^{9}+\cdots$
8112.2.a.bq	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	$\Q(\sqrt{3}) $	None	✓				78.2.i.b	$1$	$0$	$0$	$2$	$0$	$-6$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+(-3+\beta )q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots$
8112.2.a.br	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	$\Q(\sqrt{3}) $	None	✓				312.2.bf.a	$1$	$1$	$0$	$2$	$0$	$-2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+(-1-\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
8112.2.a.bs	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	$\Q(\sqrt{3}) $	None	✓				156.2.b.a	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+q^{9}+\beta q^{11}+\beta q^{15}+\cdots$
8112.2.a.bt	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	$\Q(\sqrt{3}) $	None	✓				156.2.q.a	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+2\beta q^{7}+q^{9}-2\beta q^{11}+\cdots$
8112.2.a.bu	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	$\Q(\sqrt{3}) $	None	✓				39.2.j.a	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2\beta q^{5}-\beta q^{7}+q^{9}+2\beta q^{11}+\cdots$
8112.2.a.bv	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	$\Q(\sqrt{3}) $	None	✓				39.2.b.a	$2$	$0$	$0$	$2$	$0$	$0$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}-\beta q^{7}+q^{9}-\beta q^{11}+6q^{17}+\cdots$
8112.2.a.bw	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	$\Q(\sqrt{3}) $	None	✓				312.2.bf.a	$1$	$1$	$0$	$2$	$0$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+(1-\beta )q^{7}+q^{9}+(1-\beta )q^{11}+\cdots$
8112.2.a.bx	$8112$	$2$	8112.a	1.a	$1$	$2$	$2$	$64.775$	$\Q(\sqrt{3}) $	None	✓				78.2.i.b	$1$	$0$	$0$	$2$	$0$	$6$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+(3+\beta )q^{7}+q^{9}+(3+\beta )q^{11}+\cdots$
8112.2.a.by	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	$\Q(\zeta_{14})^+$	None	✓				507.2.a.j	$1$	$1$	$0$	$-3$	$-4$	$10$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta _{1})q^{5}+(3+\beta _{1})q^{7}+\cdots$
8112.2.a.bz	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	$\Q(\zeta_{14})^+$	None	✓				1014.2.a.m	$1$	$1$	$0$	$-3$	$-3$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
8112.2.a.ca	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	$\Q(\zeta_{14})^+$	None	✓				2028.2.a.k	$1$	$1$	$0$	$-3$	$0$	$-6$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-2-\beta _{1}+\cdots)q^{7}+\cdots$
8112.2.a.cb	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	$\Q(\zeta_{14})^+$	None	✓				4056.2.a.bb	$1$	$1$	$0$	$-3$	$0$	$0$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}-\beta _{2})q^{7}+\cdots$
8112.2.a.cc	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	$\Q(\zeta_{14})^+$	None	✓				4056.2.a.bb	$1$	$0$	$0$	$-3$	$0$	$0$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1-2\beta _{1}+\beta _{2})q^{5}+(1-2\beta _{1}+\cdots)q^{7}+\cdots$
8112.2.a.cd	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	$\Q(\zeta_{14})^+$	None	✓				2028.2.a.k	$1$	$0$	$0$	$-3$	$0$	$6$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1-2\beta _{1}+\beta _{2})q^{5}+(3-2\beta _{1}+\cdots)q^{7}+\cdots$
8112.2.a.ce	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	$\Q(\zeta_{14})^+$	None	✓				1014.2.a.m	$1$	$0$	$0$	$-3$	$3$	$3$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta _{1}+\beta _{2})q^{5}+(\beta _{1}-2\beta _{2})q^{7}+\cdots$
8112.2.a.cf	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	$\Q(\zeta_{14})^+$	None	✓				507.2.a.j	$1$	$0$	$0$	$-3$	$4$	$-10$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta _{1})q^{5}+(-3-\beta _{1})q^{7}+\cdots$
8112.2.a.cg	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	$\Q(\zeta_{14})^+$	None	✓				507.2.a.i	$1$	$1$	$0$	$3$	$-6$	$2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-2+\beta _{1}+\beta _{2})q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots$
8112.2.a.ch	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	$\Q(\zeta_{14})^+$	None	✓				2028.2.a.i	$1$	$1$	$0$	$3$	$-2$	$-6$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta _{2})q^{5}+(-1-2\beta _{1}+\cdots)q^{7}+\cdots$
8112.2.a.ci	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	$\Q(\zeta_{14})^+$	None	✓				4056.2.a.x	$1$	$1$	$0$	$3$	$-2$	$0$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta _{2})q^{5}+(1-2\beta _{1}+\beta _{2})q^{7}+\cdots$
8112.2.a.cj	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	$\Q(\zeta_{14})^+$	None	✓				1014.2.a.l	$1$	$0$	$0$	$3$	$-1$	$9$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1-3\beta _{1}+\beta _{2})q^{5}+(4-\beta _{1}+\cdots)q^{7}+\cdots$
8112.2.a.ck	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	3.3.837.1	None	✓				312.2.q.e	$1$	$0$	$0$	$3$	$0$	$-3$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}-\beta _{2}q^{5}+(-1+\beta _{1})q^{7}+q^{9}+\cdots$
8112.2.a.cl	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	3.3.837.1	None	✓				312.2.q.e	$1$	$0$	$0$	$3$	$0$	$3$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{2}q^{5}+(1-\beta _{1})q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$
8112.2.a.cm	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	$\Q(\zeta_{14})^+$	None	✓				1014.2.a.l	$1$	$1$	$0$	$3$	$1$	$-9$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-\beta _{1}-2\beta _{2})q^{5}+(-2-2\beta _{1}+\cdots)q^{7}+\cdots$
8112.2.a.cn	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	$\Q(\zeta_{14})^+$	None	✓				4056.2.a.x	$1$	$0$	$0$	$3$	$2$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1-\beta _{1})q^{5}+(1-\beta _{1}+2\beta _{2})q^{7}+\cdots$
8112.2.a.co	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	$\Q(\zeta_{14})^+$	None	✓				2028.2.a.i	$1$	$0$	$0$	$3$	$2$	$6$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1-\beta _{1})q^{5}+(3-\beta _{1}+2\beta _{2})q^{7}+\cdots$
8112.2.a.cp	$8112$	$2$	8112.a	1.a	$1$	$3$	$3$	$64.775$	$\Q(\zeta_{14})^+$	None	✓				507.2.a.i	$1$	$0$	$0$	$3$	$6$	$-2$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(2-\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots$
8112.2.a.cq	$8112$	$2$	8112.a	1.a	$1$	$4$	$4$	$64.775$	$\Q(\sqrt{15 +4 \sqrt{3}})$	None	✓				312.2.bf.b	$1$	$0$	$0$	$-4$	$-4$	$2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
8112.2.a.cr	$8112$	$2$	8112.a	1.a	$1$	$4$	$4$	$64.775$	$\Q(\sqrt{3}, \sqrt{43})$	None	✓		✓		156.2.q.b	$2$	$1$	$0$	$-4$	$0$	$0$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{1}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots$
8112.2.a.cs	$8112$	$2$	8112.a	1.a	$1$	$4$	$4$	$64.775$	$\Q(\sqrt{15 +4 \sqrt{3}})$	None	✓				312.2.bf.b	$1$	$0$	$0$	$-4$	$4$	$-2$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
8112.2.a.ct	$8112$	$2$	8112.a	1.a	$1$	$6$	$6$	$64.775$	6.6.27700337.1	None	✓		✓		4056.2.a.bh	$1$	$1$	$0$	$-6$	$-1$	$-5$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(\beta _{1}-\beta _{3})q^{5}+(-1+\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots$
8112.2.a.cu	$8112$	$2$	8112.a	1.a	$1$	$6$	$6$	$64.775$	6.6.27700337.1	None	✓		✓		4056.2.a.bh	$1$	$0$	$0$	$-6$	$1$	$5$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(1-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots$
8112.2.a.cv	$8112$	$2$	8112.a	1.a	$1$	$6$	$6$	$64.775$	6.6.27700337.1	None	✓		✓		4056.2.a.bf	$1$	$0$	$0$	$6$	$-1$	$7$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-\beta _{5}q^{5}+(1+\beta _{1})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots$
8112.2.a.cw	$8112$	$2$	8112.a	1.a	$1$	$6$	$6$	$64.775$	6.6.27700337.1	None	✓		✓		4056.2.a.bf	$1$	$1$	$0$	$6$	$1$	$-7$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{5}q^{5}+(-1-\beta _{1})q^{7}+q^{9}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(8112))$ into lower level spaces

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 8112 = 2^{4} \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8112.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 75 \)
Sturm bound:			\(2912\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

\(2\)	\(3\)	\(13\)	Fricke	Total			Cusp			Eisenstein
\(2\)	\(3\)	\(13\)	Fricke	All	New	Old	All	New	Old	All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(189\)	\(18\)	\(171\)	\(169\)	\(18\)	\(151\)	\(20\)	\(0\)	\(20\)
\(+\)	\(+\)	\(-\)	\(-\)	\(195\)	\(21\)	\(174\)	\(174\)	\(21\)	\(153\)	\(21\)	\(0\)	\(21\)
\(+\)	\(-\)	\(+\)	\(-\)	\(196\)	\(23\)	\(173\)	\(175\)	\(23\)	\(152\)	\(21\)	\(0\)	\(21\)
\(+\)	\(-\)	\(-\)	\(+\)	\(190\)	\(15\)	\(175\)	\(169\)	\(15\)	\(154\)	\(21\)	\(0\)	\(21\)
\(-\)	\(+\)	\(+\)	\(-\)	\(196\)	\(18\)	\(178\)	\(175\)	\(18\)	\(157\)	\(21\)	\(0\)	\(21\)
\(-\)	\(+\)	\(-\)	\(+\)	\(190\)	\(21\)	\(169\)	\(169\)	\(21\)	\(148\)	\(21\)	\(0\)	\(21\)
\(-\)	\(-\)	\(+\)	\(+\)	\(189\)	\(18\)	\(171\)	\(168\)	\(18\)	\(150\)	\(21\)	\(0\)	\(21\)
\(-\)	\(-\)	\(-\)	\(-\)	\(195\)	\(21\)	\(174\)	\(174\)	\(21\)	\(153\)	\(21\)	\(0\)	\(21\)
Plus space			\(+\)	\(758\)	\(72\)	\(686\)	\(675\)	\(72\)	\(603\)	\(83\)	\(0\)	\(83\)
Minus space			\(-\)	\(782\)	\(83\)	\(699\)	\(698\)	\(83\)	\(615\)	\(84\)	\(0\)	\(84\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8112))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8112))\) 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	8112.2.a

Level	$8112$
Weight	$2$
Character orbit	8112.a
Rep. character	$\chi_{8112}(1,\cdot)$
Character field	$\Q$
Dimension	$155$
Newform subspaces	$75$
Sturm bound	$2912$
Trace bound	$17$