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

• Label: 375.2.i
• Level: $375$
• Weight: $2$
• Character orbit: 375.i
• Rep. character: $\chi_{375}(49,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $64$
• Newform subspaces: $4$
• Sturm bound: $100$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.i (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 4 \)
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	240	64	176
Cusp forms	160	64	96
Eisenstein series	80	0	80

Trace form

\( 64 q + 18 q^{4} - 2 q^{6} + 30 q^{8} + 16 q^{9} + O(q^{10}) \)

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.i.a	$375$	$2$	375.i	25.e	$10$	$8$	$2$	$2.994$	\(\Q(\zeta_{20})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+\zeta_{20}q^{2}+\zeta_{20}^{7}q^{3}-\zeta_{20}^{2}q^{4}+(-1+\cdots)q^{6}+\cdots\)
375.2.i.b	$375$	$2$	375.i	25.e	$10$	$16$	$4$	$2.994$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{2}$	$\mathrm{SU}(2)[C_{10}]$	\(q+\beta _{14}q^{2}+(-\beta _{1}-\beta _{5}-\beta _{6}-\beta _{13}+\cdots)q^{3}+\cdots\)
375.2.i.c	$375$	$2$	375.i	25.e	$10$	$16$	$4$	$2.994$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(\beta _{1}-\beta _{3}+\beta _{4}-\beta _{10}+\beta _{15})q^{2}+\cdots\)
375.2.i.d	$375$	$2$	375.i	25.e	$10$	$24$	$6$	$2.994$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

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

\( S_{2}^{\mathrm{old}}(375, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 2}\)