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

• Label: 325.2.e
• Level: $325$
• Weight: $2$
• Character orbit: 325.e
• Rep. character: $\chi_{325}(126,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $40$
• Newform subspaces: $5$
• Sturm bound: $70$
• Trace bound: $3$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	80	52	28
Cusp forms	56	40	16
Eisenstein series	24	12	12

Trace form

\( 40 q + 2 q^{3} - 18 q^{4} - 10 q^{6} + 2 q^{7} + 12 q^{8} - 14 q^{9} + O(q^{10}) \)

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.e.a	$325$	$2$	325.e	13.c	$3$	$4$	$2$	$2.595$	\(\Q(\sqrt{-3}, \sqrt{13})\)	None		$2$	$0$	\(-1\)	\(2\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{3}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
325.2.e.b	$325$	$2$	325.e	13.c	$3$	$4$	$2$	$2.595$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None		$2$	$0$	\(1\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(1-2\beta _{1}+\beta _{3})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
325.2.e.c	$325$	$2$	325.e	13.c	$3$	$10$	$5$	$2.595$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(-3\)	\(0\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(-1-\beta _{4}+\beta _{6}+\beta _{8})q^{3}+\cdots\)
325.2.e.d	$325$	$2$	325.e	13.c	$3$	$10$	$5$	$2.595$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(3\)	\(0\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(1+\beta _{4}-\beta _{6}-\beta _{8})q^{3}+(-\beta _{6}+\cdots)q^{4}+\cdots\)
325.2.e.e	$325$	$2$	325.e	13.c	$3$	$12$	$6$	$2.595$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{6}q^{2}+(\beta _{6}-\beta _{11})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)

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

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