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

• Label: 575.2.i
• Level: $575$
• Weight: $2$
• Character orbit: 575.i
• Rep. character: $\chi_{575}(139,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $216$
• Newform subspaces: $1$
• Sturm bound: $120$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.i (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(120\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	248	216	32
Cusp forms	232	216	16
Eisenstein series	16	0	16

Trace form

\( 216 q + 52 q^{4} + 2 q^{5} + 4 q^{6} - 30 q^{8} + 50 q^{9} + O(q^{10}) \)

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.i.a	$575$	$2$	575.i	25.e	$10$	$216$	$54$	$4.591$		None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

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

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