Space of modular forms of level 575, weight 2, and Character 575.g

• Label: 575.2.g
• Level: $575$
• Weight: $2$
• Character orbit: 575.g
• Rep. character: $\chi_{575}(116,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $224$
• Newform subspaces: $3$
• Sturm bound: $120$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.g (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(120\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(575, [\chi])\).

	Total	New	Old
Modular forms	248	224	24
Cusp forms	232	224	8
Eisenstein series	16	0	16

Trace form

\( 224 q - 2 q^{2} - 58 q^{4} - 4 q^{5} - 4 q^{6} - 8 q^{7} + 12 q^{8} - 60 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(575, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
575.2.g.a	$575$	$2$	575.g	25.d	$5$	$4$	$1$	$4.591$	\(\Q(\zeta_{10})\)	None		$2$	$1$	\(1\)	\(-5\)	\(-5\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
575.2.g.b	$575$	$2$	575.g	25.d	$5$	$108$	$27$	$4.591$		None		$2$	$0$	\(-4\)	\(1\)	\(3\)	\(24\)		$\mathrm{SU}(2)[C_{5}]$
575.2.g.c	$575$	$2$	575.g	25.d	$5$	$112$	$28$	$4.591$		None		$2$	$0$	\(1\)	\(4\)	\(-2\)	\(-36\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{2}^{\mathrm{old}}(575, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)