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

• Label: 325.2.d
• Level: $325$
• Weight: $2$
• Character orbit: 325.d
• Rep. character: $\chi_{325}(324,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $6$
• Sturm bound: $70$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(70\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	40	24	16
Cusp forms	28	20	8
Eisenstein series	12	4	8

Trace form

20 * q + 24 * q^4 - 8 * q^9 - 20 * q^14 + 20 * q^26 - 8 * q^29 - 48 * q^36 - 4 * q^39 + 56 * q^49 - 16 * q^51 - 36 * q^56 + 8 * q^61 - 64 * q^64 + 24 * q^66 + 92 * q^69 - 8 * q^74 - 68 * q^79 + 20 * q^81 + 8 * q^91 - 76 * 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.d.a	$325$	$2$	325.d	65.d	$2$	$2$	$2$	$2.595$	\(\Q(\sqrt{-1}) \)	None		✓			325.2.c.c	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2 q^{2}+i q^{3}+2 q^{4}-2 i q^{6}-2 q^{7}+\cdots\)
325.2.d.b	$325$	$2$	325.d	65.d	$2$	$2$	$2$	$2.595$	\(\Q(\sqrt{-1}) \)	None		✓			325.2.c.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+2 i q^{3}-q^{4}-2 i q^{6}+5 q^{7}+\cdots\)
325.2.d.c	$325$	$2$	325.d	65.d	$2$	$2$	$2$	$2.595$	\(\Q(\sqrt{-1}) \)	None		✓			325.2.c.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+2 i q^{3}-q^{4}+2 i q^{6}-5 q^{7}+\cdots\)
325.2.d.d	$325$	$2$	325.d	65.d	$2$	$2$	$2$	$2.595$	\(\Q(\sqrt{-1}) \)	None		✓			325.2.c.c	$2$	$0$	\(4\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 q^{2}+i q^{3}+2 q^{4}+2 i q^{6}+2 q^{7}+\cdots\)
325.2.d.e	$325$	$2$	325.d	65.d	$2$	$6$	$6$	$2.595$	6.0.5089536.1	None					65.2.c.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(2-\beta _{3})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
325.2.d.f	$325$	$2$	325.d	65.d	$2$	$6$	$6$	$2.595$	6.0.5089536.1	None					65.2.c.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(2-\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)

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

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