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

• Label: 575.2.k
• Level: $575$
• Weight: $2$
• Character orbit: 575.k
• Rep. character: $\chi_{575}(26,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $350$
• Newform subspaces: $7$
• Sturm bound: $120$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.k (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(120\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	660	410	250
Cusp forms	540	350	190
Eisenstein series	120	60	60

Trace form

350 * q + 11 * q^2 + 7 * q^3 - 25 * q^4 - 36 * q^6 + 9 * q^7 + 14 * q^8 - 26 * q^9 - 31 * q^11 - 6 * q^12 + 7 * q^13 + 11 * q^14 - 77 * q^16 + 4 * q^17 + 56 * q^18 - 20 * q^19 - 72 * q^21 - 10 * q^22 + 30 * q^23 - 42 * q^24 - 42 * q^26 - 26 * q^27 + 41 * q^28 - 4 * q^29 - 56 * q^31 - 5 * q^32 + 32 * q^33 + 3 * q^34 - 91 * q^36 + 59 * q^37 - 14 * q^38 + 71 * q^39 - 63 * q^41 + 129 * q^42 - 45 * q^43 - 182 * q^44 - 119 * q^46 + 82 * q^47 - 104 * q^48 + 22 * q^49 - 87 * q^51 + 86 * q^52 - q^53 + 112 * q^54 - 4 * q^56 + 22 * q^57 - 45 * q^58 + 73 * q^59 - 23 * q^61 - 74 * q^62 - 52 * q^63 + 122 * q^64 + 166 * q^66 - 13 * q^67 - 82 * q^68 - 150 * q^69 - 142 * q^71 - 37 * q^72 - 15 * q^73 + 132 * q^74 + 60 * q^76 - 92 * q^77 - 154 * q^78 - 9 * q^79 + 76 * q^81 - 94 * q^82 - 104 * q^83 + 5 * q^84 + 115 * q^86 - 129 * q^87 - 11 * q^88 - 65 * q^89 - 48 * q^91 - 94 * q^92 - 152 * q^93 - 105 * q^94 + 149 * q^96 - 22 * q^97 - 5 * q^98 - 30 * q^99

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.k.a	$575$	$2$	575.k	23.c	$11$	$10$	$1$	$4.591$	\(\Q(\zeta_{22})\)	None					115.2.g.a	$2$	$0$	\(-5\)	\(-1\)	\(0\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(-\zeta_{22}-\zeta_{22}^{3}+\zeta_{22}^{4}-\zeta_{22}^{5}+\cdots)q^{2}+\cdots\)
575.2.k.b	$575$	$2$	575.k	23.c	$11$	$10$	$1$	$4.591$	\(\Q(\zeta_{22})\)	None					23.2.c.a	$2$	$0$	\(7\)	\(7\)	\(0\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(1-\zeta_{22}-\zeta_{22}^{7}+\zeta_{22}^{8})q^{2}+(1+\cdots)q^{3}+\cdots\)
575.2.k.c	$575$	$2$	575.k	23.c	$11$	$20$	$2$	$4.591$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None					115.2.g.b	$2$	$0$	\(4\)	\(-1\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(1-\beta _{2}-\beta _{3}-\beta _{4}-\beta _{6}-\beta _{8}+\beta _{13}+\cdots)q^{2}+\cdots\)
575.2.k.d	$575$	$2$	575.k	23.c	$11$	$50$	$5$	$4.591$		None					115.2.g.c	$2$	$0$	\(5\)	\(2\)	\(0\)	\(5\)		$\mathrm{SU}(2)[C_{11}]$
575.2.k.e	$575$	$2$	575.k	23.c	$11$	$80$	$8$	$4.591$		None		✓			575.2.k.e	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{11}]$
575.2.k.f	$575$	$2$	575.k	23.c	$11$	$80$	$8$	$4.591$		None		✓			575.2.k.e	$2$	$0$	\(2\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{11}]$
575.2.k.g	$575$	$2$	575.k	23.c	$11$	$100$	$10$	$4.591$		None			✓		115.2.j.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{11}]$

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

\( S_{2}^{\mathrm{old}}(575, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)