Space of modular forms of level 375, weight 2, and Character 375.m

• Label: 375.2.m
• Level: $375$
• Weight: $2$
• Character orbit: 375.m
• Rep. character: $\chi_{375}(16,\cdot)$
• Character field: $\Q(\zeta_{25})$
• Dimension: $520$
• Newform subspaces: $2$
• Sturm bound: $100$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.m (of order \(25\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 125 \)
Character field:			\(\Q(\zeta_{25})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(100\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(375, [\chi])\).

	Total	New	Old
Modular forms	1040	520	520
Cusp forms	960	520	440
Eisenstein series	80	0	80

Trace form

\( 520 q - 30 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(375, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
375.2.m.a	$375$	$2$	375.m	125.g	$25$	$260$	$13$	$2.994$		None		$2$	$0$	\(0\)	\(0\)	\(20\)	\(-10\)		$\mathrm{SU}(2)[C_{25}]$
375.2.m.b	$375$	$2$	375.m	125.g	$25$	$260$	$13$	$2.994$		None		$2$	$0$	\(0\)	\(0\)	\(-20\)	\(10\)		$\mathrm{SU}(2)[C_{25}]$

Decomposition of \(S_{2}^{\mathrm{old}}(375, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(375, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 2}\)