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

• Label: 325.2.n
• Level: $325$
• Weight: $2$
• Character orbit: 325.n
• Rep. character: $\chi_{325}(101,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $38$
• Newform subspaces: $6$
• Sturm bound: $70$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
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	84	50	34
Cusp forms	60	38	22
Eisenstein series	24	12	12

Trace form

\( 38 q + 3 q^{2} + 17 q^{4} + 6 q^{7} - 13 q^{9} + O(q^{10}) \)

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.n.a	$325$	$2$	325.n	13.e	$6$	$2$	$1$	$2.595$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(3\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
325.2.n.b	$325$	$2$	325.n	13.e	$6$	$4$	$2$	$2.595$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		$2$	$0$	\(-3\)	\(2\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{3})q^{2}+\beta _{2}q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
325.2.n.c	$325$	$2$	325.n	13.e	$6$	$4$	$2$	$2.595$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		$2$	$0$	\(3\)	\(-2\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{3})q^{2}-\beta _{2}q^{3}+(\beta _{1}+\beta _{2}-2\beta _{3})q^{4}+\cdots\)
325.2.n.d	$325$	$2$	325.n	13.e	$6$	$8$	$4$	$2.595$	8.0.22581504.2	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{3}+\beta _{5}+\beta _{7})q^{2}+(-1+\beta _{1}+2\beta _{2}+\cdots)q^{3}+\cdots\)
325.2.n.e	$325$	$2$	325.n	13.e	$6$	$10$	$5$	$2.595$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(-3\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{3}q^{2}+(-1-\beta _{2}-\beta _{8}+\beta _{9})q^{3}+\cdots\)
325.2.n.f	$325$	$2$	325.n	13.e	$6$	$10$	$5$	$2.595$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(3\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}+\beta _{3})q^{2}+(-\beta _{2}+\beta _{9})q^{3}+(2+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(325, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)