Space of modular forms of level 2925, weight 2, and Character 2925.c

• Label: 2925.2.c
• Level: $2925$
• Weight: $2$
• Character orbit: 2925.c
• Rep. character: $\chi_{2925}(2224,\cdot)$
• Character field: $\Q$
• Dimension: $90$
• Newform subspaces: $26$
• Sturm bound: $840$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 2925 = 3^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2925.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 26 \)
Sturm bound:			\(840\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2925, [\chi])\).

	Total	New	Old
Modular forms	444	90	354
Cusp forms	396	90	306
Eisenstein series	48	0	48

Trace form

90 * q - 98 * q^4 - 4 * q^11 - 20 * q^14 + 106 * q^16 - 24 * q^19 - 6 * q^26 - 20 * q^29 + 24 * q^31 + 32 * q^34 - 16 * q^41 - 36 * q^44 - 28 * q^46 - 46 * q^49 + 116 * q^56 + 32 * q^59 + 4 * q^61 - 178 * q^64 - 68 * q^71 - 84 * q^74 + 104 * q^76 - 12 * q^79 - 44 * q^86 - 8 * q^89 + 16 * q^91 - 28 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(2925, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2925.2.c.a	$2925$	$2$	2925.c	5.b	$2$	$2$	$2$	$23.356$	\(\Q(\sqrt{-1}) \)	None					195.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}-2 q^{4}+i q^{7}-5 q^{11}+\cdots\)
2925.2.c.b	$2925$	$2$	2925.c	5.b	$2$	$2$	$2$	$23.356$	\(\Q(\sqrt{-1}) \)	None					325.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}-2 q^{4}-2 i q^{7}-2 q^{11}+\cdots\)
2925.2.c.c	$2925$	$2$	2925.c	5.b	$2$	$2$	$2$	$23.356$	\(\Q(\sqrt{-1}) \)	None					195.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}-2 q^{4}-3 i q^{7}+q^{11}+\cdots\)
2925.2.c.d	$2925$	$2$	2925.c	5.b	$2$	$2$	$2$	$23.356$	\(\Q(\sqrt{-1}) \)	None					195.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}-2 q^{4}+3 i q^{7}+5 q^{11}+\cdots\)
2925.2.c.e	$2925$	$2$	2925.c	5.b	$2$	$2$	$2$	$23.356$	\(\Q(\sqrt{-1}) \)	None					39.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{4}+4 i q^{7}+3 i q^{8}-4 q^{11}+\cdots\)
2925.2.c.f	$2925$	$2$	2925.c	5.b	$2$	$2$	$2$	$23.356$	\(\Q(\sqrt{-1}) \)	None					195.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{4}+3 i q^{8}-4 q^{11}-i q^{13}+\cdots\)
2925.2.c.g	$2925$	$2$	2925.c	5.b	$2$	$2$	$2$	$23.356$	\(\Q(\sqrt{-1}) \)	None					585.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{4}-2 i q^{7}+3 i q^{8}-4 q^{11}+\cdots\)
2925.2.c.h	$2925$	$2$	2925.c	5.b	$2$	$2$	$2$	$23.356$	\(\Q(\sqrt{-1}) \)	None					65.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{4}-4 i q^{7}+3 i q^{8}-2 q^{11}+\cdots\)
2925.2.c.i	$2925$	$2$	2925.c	5.b	$2$	$2$	$2$	$23.356$	\(\Q(\sqrt{-1}) \)	None					975.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{4}+3 i q^{7}+3 i q^{8}+q^{11}+\cdots\)
2925.2.c.j	$2925$	$2$	2925.c	5.b	$2$	$2$	$2$	$23.356$	\(\Q(\sqrt{-1}) \)	None					975.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{4}-i q^{7}+3 i q^{8}+q^{11}+\cdots\)
2925.2.c.k	$2925$	$2$	2925.c	5.b	$2$	$2$	$2$	$23.356$	\(\Q(\sqrt{-1}) \)	None					585.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{4}+2 i q^{7}+3 i q^{8}+4 q^{11}+\cdots\)
2925.2.c.l	$2925$	$2$	2925.c	5.b	$2$	$2$	$2$	$23.356$	\(\Q(\sqrt{-1}) \)	None					585.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 q^{4}-i q^{7}-3 q^{11}-i q^{13}+4 q^{16}+\cdots\)
2925.2.c.m	$2925$	$2$	2925.c	5.b	$2$	$2$	$2$	$23.356$	\(\Q(\sqrt{-1}) \)	None					585.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 q^{4}-i q^{7}+3 q^{11}-i q^{13}+4 q^{16}+\cdots\)
2925.2.c.n	$2925$	$2$	2925.c	5.b	$2$	$2$	$2$	$23.356$	\(\Q(\sqrt{-1}) \)	None					325.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 q^{4}-4 i q^{7}+6 q^{11}-i q^{13}+\cdots\)
2925.2.c.o	$2925$	$2$	2925.c	5.b	$2$	$4$	$4$	$23.356$	\(\Q(i, \sqrt{17})\)	None					585.2.a.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-3+\beta _{3})q^{4}+(-\beta _{1}-3\beta _{2}+\cdots)q^{7}+\cdots\)
2925.2.c.p	$2925$	$2$	2925.c	5.b	$2$	$4$	$4$	$23.356$	\(\Q(i, \sqrt{17})\)	None					585.2.a.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-3+\beta _{3})q^{4}+(\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots\)
2925.2.c.q	$2925$	$2$	2925.c	5.b	$2$	$4$	$4$	$23.356$	\(\Q(\zeta_{8})\)	None					325.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}+\beta_1)q^{2}+(-2\beta_{3}-1)q^{4}+\cdots\)
2925.2.c.r	$2925$	$2$	2925.c	5.b	$2$	$4$	$4$	$23.356$	\(\Q(\zeta_{8})\)	None					65.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}+\beta_1)q^{2}+(-2\beta_{3}-1)q^{4}+\cdots\)
2925.2.c.s	$2925$	$2$	2925.c	5.b	$2$	$4$	$4$	$23.356$	\(\Q(\zeta_{12})\)	None					117.2.a.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{2} q^{2}-q^{4}+2\beta_1 q^{7}+\beta_{2} q^{8}+\cdots\)
2925.2.c.t	$2925$	$2$	2925.c	5.b	$2$	$4$	$4$	$23.356$	\(\Q(\zeta_{12})\)	None		✓			2925.2.a.ba	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{2} q^{2}-q^{4}+\beta_1 q^{7}-\beta_{2} q^{8}+\cdots\)
2925.2.c.u	$2925$	$2$	2925.c	5.b	$2$	$4$	$4$	$23.356$	\(\Q(\zeta_{8})\)	None					39.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}+\beta_1)q^{2}+(-2\beta_{3}-1)q^{4}+\cdots\)
2925.2.c.v	$2925$	$2$	2925.c	5.b	$2$	$4$	$4$	$23.356$	\(\Q(\zeta_{12})\)	None					65.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{2} q^{2}-q^{4}-2\beta_1 q^{7}+\beta_{2} q^{8}+\cdots\)
2925.2.c.w	$2925$	$2$	2925.c	5.b	$2$	$6$	$6$	$23.356$	6.0.399424.1	None					195.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+(-3+\beta _{4})q^{4}-\beta _{5}q^{7}+(2\beta _{2}+\cdots)q^{8}+\cdots\)
2925.2.c.x	$2925$	$2$	2925.c	5.b	$2$	$6$	$6$	$23.356$	6.0.5089536.1	None					975.2.a.n	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+(-2+\beta _{3})q^{4}+(2\beta _{4}-\beta _{5})q^{7}+\cdots\)
2925.2.c.y	$2925$	$2$	2925.c	5.b	$2$	$6$	$6$	$23.356$	6.0.350464.1	None					975.2.a.m	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2})q^{4}+\cdots\)
2925.2.c.z	$2925$	$2$	2925.c	5.b	$2$	$12$	$12$	$23.356$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓		2925.2.a.bp	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+(-2+\beta _{1})q^{4}+(\beta _{4}+\beta _{9}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2925, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2925, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 2}\)