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

• Label: 575.2.e
• Level: $575$
• Weight: $2$
• Character orbit: 575.e
• Rep. character: $\chi_{575}(68,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $68$
• Newform subspaces: $5$
• Sturm bound: $120$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 115 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 5 \)
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	132	76	56
Cusp forms	108	68	40
Eisenstein series	24	8	16

Trace form

68 * q + 4 * q^2 + 8 * q^3 - 8 * q^6 - 4 * q^8 + 16 * q^12 - 4 * q^13 - 112 * q^16 - 8 * q^18 + 8 * q^26 - 4 * q^27 - 16 * q^31 - 24 * q^32 + 184 * q^36 + 48 * q^41 - 16 * q^46 + 8 * q^47 - 4 * q^48 - 40 * q^52 - 36 * q^58 + 60 * q^62 + 8 * q^71 - 72 * q^72 + 56 * q^73 + 12 * q^77 + 44 * q^78 - 340 * q^81 - 28 * q^82 - 24 * q^87 + 72 * q^92 + 8 * q^93 - 104 * q^96 + 60 * q^98

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
575.2.e.a	$575$	$2$	575.e	115.e	$4$	$4$	$2$	$4.591$	\(\Q(i, \sqrt{46})\)	\(\Q(\sqrt{-115}) \)		✓			575.2.e.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+2\beta _{2}q^{4}+\beta _{1}q^{7}-3\beta _{2}q^{9}-4q^{16}+\cdots\)
575.2.e.b	$575$	$2$	575.e	115.e	$4$	$8$	$4$	$4.591$	8.0.\(\cdots\).1	None		✓			575.2.e.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{2}q^{2}+\beta _{1}q^{4}-\beta _{7}q^{7}+\beta _{5}q^{8}+\cdots\)
575.2.e.c	$575$	$2$	575.e	115.e	$4$	$12$	$6$	$4.591$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	\(\Q(\sqrt{-23}) \)		✓			575.2.e.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+\beta _{1}q^{2}-\beta _{10}q^{3}+(\beta _{6}-2\beta _{7}+\beta _{9}+\cdots)q^{4}+\cdots\)
575.2.e.d	$575$	$2$	575.e	115.e	$4$	$20$	$10$	$4.591$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None					115.2.e.a	$4$	$0$	\(4\)	\(8\)	\(0\)	\(0\)	$2^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{3}q^{2}-\beta _{2}q^{3}+\beta _{4}q^{4}+(-1+\beta _{3}+\cdots)q^{6}+\cdots\)
575.2.e.e	$575$	$2$	575.e	115.e	$4$	$24$	$12$	$4.591$		\(\Q(\sqrt{-23}) \)		✓	✓		575.2.e.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{U}(1)[D_{4}]$

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

\( S_{2}^{\mathrm{old}}(575, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)