Space of modular forms of level 325, weight 2, and Character 325.c

• Label: 325.2.c
• Level: $325$
• Weight: $2$
• Character orbit: 325.c
• Rep. character: $\chi_{325}(51,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $7$
• Sturm bound: $70$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(70\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(2\), \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(325, [\chi])\).

	Total	New	Old
Modular forms	42	24	18
Cusp forms	30	18	12
Eisenstein series	12	6	6

Trace form

18 * q + 4 * q^3 - 10 * q^4 + 6 * q^9 + 8 * q^13 + 12 * q^14 - 14 * q^16 - 8 * q^17 + 24 * q^22 - 16 * q^23 - 6 * q^26 + 28 * q^27 - 12 * q^29 - 10 * q^36 + 20 * q^38 + 4 * q^39 - 44 * q^42 - 24 * q^43 - 36 * q^48 - 30 * q^49 - 24 * q^51 - 20 * q^52 - 12 * q^53 + 12 * q^56 + 44 * q^61 - 8 * q^62 + 6 * q^64 + 16 * q^66 + 88 * q^68 - 12 * q^69 + 12 * q^74 - 36 * q^77 + 52 * q^78 + 44 * q^79 - 54 * q^81 + 28 * q^82 + 4 * q^87 - 60 * q^88 - 24 * q^91 + 20 * q^92 + 52 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(325, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
325.2.c.a	$325$	$2$	325.c	13.b	$2$	$2$	$2$	$2.595$	\(\Q(\sqrt{-1}) \)	None		✓			325.2.c.a	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-2 q^{3}+q^{4}-2 i q^{6}-5 i q^{7}+\cdots\)
325.2.c.b	$325$	$2$	325.c	13.b	$2$	$2$	$2$	$2.595$	\(\Q(\sqrt{-1}) \)	None					65.2.d.a	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-2 q^{3}+q^{4}-2 i q^{6}+3 i q^{8}+\cdots\)
325.2.c.c	$325$	$2$	325.c	13.b	$2$	$2$	$2$	$2.595$	\(\Q(\sqrt{-1}) \)	None		✓			325.2.c.c	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-q^{3}-2 q^{4}-\beta q^{6}+\beta q^{7}+\cdots\)
325.2.c.d	$325$	$2$	325.c	13.b	$2$	$2$	$2$	$2.595$	\(\Q(\sqrt{-1}) \)	None		✓			325.2.c.c	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+q^{3}-2 q^{4}+\beta q^{6}+\beta q^{7}+\cdots\)
325.2.c.e	$325$	$2$	325.c	13.b	$2$	$2$	$2$	$2.595$	\(\Q(\sqrt{-1}) \)	None					65.2.d.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+2 q^{3}+q^{4}+2 i q^{6}+3 i q^{8}+\cdots\)
325.2.c.f	$325$	$2$	325.c	13.b	$2$	$2$	$2$	$2.595$	\(\Q(\sqrt{-1}) \)	None		✓			325.2.c.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+2 q^{3}+q^{4}+2 i q^{6}-5 i q^{7}+\cdots\)
325.2.c.g	$325$	$2$	325.c	13.b	$2$	$6$	$6$	$2.595$	6.0.5089536.1	None			✓		65.2.c.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(1+\beta _{1})q^{3}+(-2+\beta _{3})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(325, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(325, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)