Space of modular forms of level 3025, weight 2, and trivial character

• Label: 3025.2.a
• Level: $3025$
• Weight: $2$
• Character orbit: 3025.a
• Rep. character: $\chi_{3025}(1,\cdot)$
• Character field: $\Q$
• Dimension: $159$
• Newform subspaces: $41$
• Sturm bound: $660$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 3025 = 5^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3025.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 41 \)
Sturm bound:			\(660\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\), \(3\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3025))\).

	Total	New	Old
Modular forms	366	186	180
Cusp forms	295	159	136
Eisenstein series	71	27	44

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

\(5\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(37\)
\(+\)	\(-\)	\(-\)	\(40\)
\(-\)	\(+\)	\(-\)	\(44\)
\(-\)	\(-\)	\(+\)	\(38\)
Plus space		\(+\)	\(75\)
Minus space		\(-\)	\(84\)

Trace form

159 * q + q^2 - 2 * q^3 + 147 * q^4 + 2 * q^6 - 6 * q^7 + 3 * q^8 + 133 * q^9 - 12 * q^12 - 2 * q^13 + 4 * q^14 + 123 * q^16 + 12 * q^17 + 11 * q^18 - 8 * q^19 + 6 * q^21 + 14 * q^23 + 16 * q^24 - 4 * q^26 - 2 * q^27 - 8 * q^28 + 6 * q^29 - 2 * q^31 + 7 * q^32 + 40 * q^34 + 123 * q^36 - 2 * q^37 + 8 * q^38 - 24 * q^39 + 2 * q^41 + 56 * q^42 - 14 * q^43 + 30 * q^46 - 4 * q^47 + 24 * q^48 + 59 * q^49 + 2 * q^51 + 14 * q^52 - 4 * q^53 + 6 * q^54 - 20 * q^56 - 12 * q^58 + 18 * q^59 + 6 * q^61 - 22 * q^62 - 16 * q^63 + 63 * q^64 - 14 * q^67 + 14 * q^68 + 46 * q^69 + 18 * q^71 + 39 * q^72 + 10 * q^73 - 24 * q^74 + 8 * q^76 + 40 * q^78 - 22 * q^79 + 95 * q^81 + 16 * q^82 - 22 * q^83 + 64 * q^84 + 68 * q^86 + 32 * q^87 + 54 * q^89 - 88 * q^91 - 46 * q^93 - 64 * q^94 - 4 * q^96 - 30 * q^97 - 7 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3025))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	11
3025.2.a.a	$3025$	$2$	3025.a	1.a	$1$	$1$	$1$	$24.155$	\(\Q\)	None	✓				11.2.a.a	$1$	$0$	\(-2\)	\(1\)	\(0\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+2q^{4}-2q^{6}-2q^{7}+\cdots\)
3025.2.a.b	$3025$	$2$	3025.a	1.a	$1$	$1$	$1$	$24.155$	\(\Q\)	None	✓				121.2.a.a	$1$	$0$	\(-1\)	\(-2\)	\(0\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}-q^{4}+2q^{6}+2q^{7}+3q^{8}+\cdots\)
3025.2.a.c	$3025$	$2$	3025.a	1.a	$1$	$1$	$1$	$24.155$	\(\Q\)	None	✓				605.2.a.a	$1$	$0$	\(-1\)	\(3\)	\(0\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}-q^{4}-3q^{6}-3q^{7}+3q^{8}+\cdots\)
3025.2.a.d	$3025$	$2$	3025.a	1.a	$1$	$1$	$1$	$24.155$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓				121.2.a.b	$2$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+q^{3}-2q^{4}-2q^{9}-2q^{12}+4q^{16}+\cdots\)
3025.2.a.e	$3025$	$2$	3025.a	1.a	$1$	$1$	$1$	$24.155$	\(\Q\)	None	✓				121.2.a.a	$1$	$0$	\(1\)	\(-2\)	\(0\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}-q^{4}-2q^{6}-2q^{7}-3q^{8}+\cdots\)
3025.2.a.f	$3025$	$2$	3025.a	1.a	$1$	$1$	$1$	$24.155$	\(\Q\)	None	✓				55.2.a.a	$1$	$0$	\(1\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-3q^{8}-3q^{9}+2q^{13}+\cdots\)
3025.2.a.g	$3025$	$2$	3025.a	1.a	$1$	$1$	$1$	$24.155$	\(\Q\)	None	✓				605.2.a.a	$1$	$0$	\(1\)	\(3\)	\(0\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+3q^{3}-q^{4}+3q^{6}+3q^{7}-3q^{8}+\cdots\)
3025.2.a.h	$3025$	$2$	3025.a	1.a	$1$	$2$	$2$	$24.155$	\(\Q(\sqrt{13}) \)	None	✓				275.2.a.e	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(-5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(1-\beta )q^{3}+(1+\beta )q^{4}+3q^{6}+\cdots\)
3025.2.a.i	$3025$	$2$	3025.a	1.a	$1$	$2$	$2$	$24.155$	\(\Q(\sqrt{5}) \)	None	✓				275.2.a.d	$1$	$0$	\(-1\)	\(3\)	\(0\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(1+\beta )q^{3}+(-1+\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
3025.2.a.j	$3025$	$2$	3025.a	1.a	$1$	$2$	$2$	$24.155$	\(\Q(\sqrt{3}) \)	None	✓				605.2.a.f	$2$	$1$	\(0\)	\(-4\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-2q^{3}+q^{4}-2\beta q^{6}+2\beta q^{7}+\cdots\)
3025.2.a.k	$3025$	$2$	3025.a	1.a	$1$	$2$	$2$	$24.155$	\(\Q(\sqrt{11}) \)	\(\Q(\sqrt{-11}) \)	✓				605.2.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-\beta q^{3}-2q^{4}+8q^{9}+2\beta q^{12}+4q^{16}+\cdots\)
3025.2.a.l	$3025$	$2$	3025.a	1.a	$1$	$2$	$2$	$24.155$	\(\Q(\sqrt{3}) \)	None	✓				605.2.a.e	$2$	$1$	\(0\)	\(2\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+q^{4}+\beta q^{6}-\beta q^{7}-\beta q^{8}+\cdots\)
3025.2.a.m	$3025$	$2$	3025.a	1.a	$1$	$2$	$2$	$24.155$	\(\Q(\sqrt{5}) \)	None	✓				275.2.a.d	$1$	$1$	\(1\)	\(-3\)	\(0\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1-\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
3025.2.a.n	$3025$	$2$	3025.a	1.a	$1$	$2$	$2$	$24.155$	\(\Q(\sqrt{13}) \)	None	✓				275.2.a.e	$1$	$0$	\(1\)	\(-1\)	\(0\)	\(5\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{3}+(1+\beta )q^{4}+3q^{6}+\cdots\)
3025.2.a.o	$3025$	$2$	3025.a	1.a	$1$	$2$	$2$	$24.155$	\(\Q(\sqrt{2}) \)	None	✓				55.2.a.b	$1$	$0$	\(2\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+2\beta q^{3}+(1+2\beta )q^{4}+(4+\cdots)q^{6}+\cdots\)
3025.2.a.p	$3025$	$2$	3025.a	1.a	$1$	$3$	$3$	$24.155$	3.3.404.1	None	✓				605.2.a.g	$1$	$0$	\(-1\)	\(-1\)	\(0\)	\(1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}-\beta _{1}q^{3}+(3+\beta _{1}-\beta _{2})q^{4}+\cdots\)
3025.2.a.q	$3025$	$2$	3025.a	1.a	$1$	$3$	$3$	$24.155$	3.3.473.1	None	✓	✓			3025.2.a.q	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1-\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
3025.2.a.r	$3025$	$2$	3025.a	1.a	$1$	$3$	$3$	$24.155$	3.3.473.1	None	✓	✓			3025.2.a.q	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1-\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
3025.2.a.s	$3025$	$2$	3025.a	1.a	$1$	$3$	$3$	$24.155$	3.3.473.1	None	✓	✓			3025.2.a.q	$1$	$0$	\(0\)	\(3\)	\(0\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
3025.2.a.t	$3025$	$2$	3025.a	1.a	$1$	$3$	$3$	$24.155$	3.3.473.1	None	✓	✓			3025.2.a.q	$1$	$0$	\(0\)	\(3\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
3025.2.a.u	$3025$	$2$	3025.a	1.a	$1$	$3$	$3$	$24.155$	3.3.404.1	None	✓				605.2.a.g	$1$	$0$	\(1\)	\(-1\)	\(0\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(3+\beta _{1}-\beta _{2})q^{4}+\cdots\)
3025.2.a.v	$3025$	$2$	3025.a	1.a	$1$	$4$	$4$	$24.155$	4.4.2525.1	None	✓				55.2.g.a	$1$	$1$	\(-3\)	\(2\)	\(0\)	\(-11\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{3})q^{2}+\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
3025.2.a.w	$3025$	$2$	3025.a	1.a	$1$	$4$	$4$	$24.155$	4.4.725.1	None	✓				55.2.g.b	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1-\beta _{2}-\beta _{3})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
3025.2.a.x	$3025$	$2$	3025.a	1.a	$1$	$4$	$4$	$24.155$	4.4.105840.1	None	✓	✓			3025.2.a.x	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(3+\beta _{2})q^{4}+\cdots\)
3025.2.a.y	$3025$	$2$	3025.a	1.a	$1$	$4$	$4$	$24.155$	\(\Q(\zeta_{24})^+\)	None	✓				605.2.b.d	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}-q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
3025.2.a.z	$3025$	$2$	3025.a	1.a	$1$	$4$	$4$	$24.155$	\(\Q(\zeta_{24})^+\)	None	✓				605.2.b.d	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{2}q^{4}+q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
3025.2.a.ba	$3025$	$2$	3025.a	1.a	$1$	$4$	$4$	$24.155$	\(\Q(\sqrt{3}, \sqrt{11})\)	None	✓				55.2.b.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(2+\beta _{3})q^{4}+\cdots\)
3025.2.a.bb	$3025$	$2$	3025.a	1.a	$1$	$4$	$4$	$24.155$	4.4.4400.1	\(\Q(\sqrt{-55}) \)	✓				605.2.b.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{2}$	$N(\mathrm{U}(1))$	\(q-\beta _{2}q^{2}+(2-\beta _{3})q^{4}+\beta _{1}q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots\)
3025.2.a.bc	$3025$	$2$	3025.a	1.a	$1$	$4$	$4$	$24.155$	4.4.105840.1	None	✓	✓			3025.2.a.x	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{3}+(3+\beta _{2})q^{4}+\cdots\)
3025.2.a.bd	$3025$	$2$	3025.a	1.a	$1$	$4$	$4$	$24.155$	4.4.725.1	None	✓				55.2.g.b	$1$	$1$	\(1\)	\(0\)	\(0\)	\(3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1-\beta _{2}-\beta _{3})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
3025.2.a.be	$3025$	$2$	3025.a	1.a	$1$	$4$	$4$	$24.155$	4.4.2525.1	None	✓				55.2.g.a	$1$	$0$	\(3\)	\(2\)	\(0\)	\(11\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2}-\beta _{3})q^{2}+(1-\beta _{1})q^{3}+(2+\cdots)q^{4}+\cdots\)
3025.2.a.bf	$3025$	$2$	3025.a	1.a	$1$	$6$	$6$	$24.155$	\(\Q(\zeta_{36})^+\)	None	✓	✓			3025.2.a.bf	$2$	$1$	\(0\)	\(-6\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
3025.2.a.bg	$3025$	$2$	3025.a	1.a	$1$	$6$	$6$	$24.155$	6.6.27433728.1	None	✓				605.2.a.m	$2$	$1$	\(0\)	\(-6\)	\(0\)	\(0\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
3025.2.a.bh	$3025$	$2$	3025.a	1.a	$1$	$6$	$6$	$24.155$	\(\Q(\zeta_{36})^+\)	None	✓	✓			3025.2.a.bf	$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
3025.2.a.bi	$3025$	$2$	3025.a	1.a	$1$	$8$	$8$	$24.155$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		275.2.h.c	$1$	$1$	\(-5\)	\(-1\)	\(0\)	\(-8\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+\beta _{5}q^{3}+(1-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
3025.2.a.bj	$3025$	$2$	3025.a	1.a	$1$	$8$	$8$	$24.155$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				275.2.h.c	$1$	$1$	\(-5\)	\(1\)	\(0\)	\(-8\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-\beta _{5}q^{3}+(1-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
3025.2.a.bk	$3025$	$2$	3025.a	1.a	$1$	$8$	$8$	$24.155$	8.8.1480160000.1	None	✓				55.2.j.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{6}-\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots\)
3025.2.a.bl	$3025$	$2$	3025.a	1.a	$1$	$8$	$8$	$24.155$	8.8.1480160000.1	None	✓				55.2.j.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{6}+\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots\)
3025.2.a.bm	$3025$	$2$	3025.a	1.a	$1$	$8$	$8$	$24.155$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		275.2.h.c	$1$	$0$	\(5\)	\(-1\)	\(0\)	\(8\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+\beta _{5}q^{3}+(1-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
3025.2.a.bn	$3025$	$2$	3025.a	1.a	$1$	$8$	$8$	$24.155$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				275.2.h.c	$1$	$0$	\(5\)	\(1\)	\(0\)	\(8\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}-\beta _{5}q^{3}+(1-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
3025.2.a.bo	$3025$	$2$	3025.a	1.a	$1$	$12$	$12$	$24.155$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		605.2.b.h	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(2-\beta _{10})q^{4}+\beta _{2}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3025))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3025)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(605))\)\(^{\oplus 2}\)