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

• Label: 325.2.b
• Level: $325$
• Weight: $2$
• Character orbit: 325.b
• Rep. character: $\chi_{325}(274,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $6$
• Sturm bound: $70$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(70\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

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

	Total	New	Old
Modular forms	42	18	24
Cusp forms	30	18	12
Eisenstein series	12	0	12

Trace form

\( 18 q - 10 q^{4} - 12 q^{6} - 14 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
325.2.b.a	$325$	$2$	325.b	5.b	$2$	$2$	$2$	$2.595$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-iq^{3}-2q^{4}+2q^{6}+2iq^{7}+\cdots\)
325.2.b.b	$325$	$2$	325.b	5.b	$2$	$2$	$2$	$2.595$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-2iq^{3}+q^{4}+2q^{6}+4iq^{7}+\cdots\)
325.2.b.c	$325$	$2$	325.b	5.b	$2$	$2$	$2$	$2.595$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2q^{4}+4iq^{7}+2q^{9}-6q^{11}+\cdots\)
325.2.b.d	$325$	$2$	325.b	5.b	$2$	$4$	$4$	$2.595$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+2\zeta_{8}^{2}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
325.2.b.e	$325$	$2$	325.b	5.b	$2$	$4$	$4$	$2.595$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{2}q^{2}+(-\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots\)
325.2.b.f	$325$	$2$	325.b	5.b	$2$	$4$	$4$	$2.595$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}-\zeta_{8}^{2}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)

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

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