Space of modular forms of level 575, weight 4, and Character 575.b

• Label: 575.4.b
• Level: $575$
• Weight: $4$
• Character orbit: 575.b
• Rep. character: $\chi_{575}(24,\cdot)$
• Character field: $\Q$
• Dimension: $98$
• Newform subspaces: $12$
• Sturm bound: $240$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	575.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(240\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(575, [\chi])\).

	Total	New	Old
Modular forms	186	98	88
Cusp forms	174	98	76
Eisenstein series	12	0	12

Trace form

98 * q - 384 * q^4 - 24 * q^6 - 910 * q^9 + 16 * q^11 - 340 * q^14 + 1728 * q^16 + 72 * q^19 - 224 * q^21 - 476 * q^24 - 208 * q^26 + 356 * q^29 + 340 * q^31 + 72 * q^34 + 3192 * q^36 + 656 * q^39 + 176 * q^41 + 2692 * q^44 - 184 * q^46 - 5794 * q^49 - 1268 * q^51 - 608 * q^54 + 3544 * q^56 + 972 * q^59 + 1856 * q^61 - 10508 * q^64 + 1540 * q^66 + 552 * q^69 - 2076 * q^71 - 4296 * q^74 - 2916 * q^76 - 2224 * q^79 + 5810 * q^81 + 4020 * q^84 + 10216 * q^86 - 5120 * q^89 + 1280 * q^91 + 2524 * q^94 - 3456 * q^96 - 556 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(575, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
575.4.b.a	$575$	$4$	575.b	5.b	$2$	$2$	$2$	$33.926$	\(\Q(\sqrt{-1}) \)	None					115.4.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}+3 i q^{3}+4 q^{4}-6 q^{6}+\cdots\)
575.4.b.b	$575$	$4$	575.b	5.b	$2$	$2$	$2$	$33.926$	\(\Q(\sqrt{-1}) \)	None					23.4.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}-5 i q^{3}+4 q^{4}+10 q^{6}+\cdots\)
575.4.b.c	$575$	$4$	575.b	5.b	$2$	$2$	$2$	$33.926$	\(\Q(\sqrt{-1}) \)	None		✓			575.4.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+10 i q^{3}+7 q^{4}-10 q^{6}+\cdots\)
575.4.b.d	$575$	$4$	575.b	5.b	$2$	$2$	$2$	$33.926$	\(\Q(\sqrt{-1}) \)	None		✓			575.4.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+6 i q^{3}+7 q^{4}-6 q^{6}-7 i q^{7}+\cdots\)
575.4.b.e	$575$	$4$	575.b	5.b	$2$	$2$	$2$	$33.926$	\(\Q(\sqrt{-1}) \)	None					115.4.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-4 i q^{3}+7 q^{4}+4 q^{6}-32 i q^{7}+\cdots\)
575.4.b.f	$575$	$4$	575.b	5.b	$2$	$4$	$4$	$33.926$	\(\Q(i, \sqrt{109})\)	None					115.4.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\beta _{2}q^{2}+(-\beta _{1}+\beta _{2})q^{3}-q^{4}+(6+\cdots)q^{6}+\cdots\)
575.4.b.g	$575$	$4$	575.b	5.b	$2$	$8$	$8$	$33.926$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					23.4.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}-\beta _{6})q^{2}+(-\beta _{1}+\beta _{6}-\beta _{7})q^{3}+\cdots\)
575.4.b.h	$575$	$4$	575.b	5.b	$2$	$10$	$10$	$33.926$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None					115.4.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{5})q^{2}+(\beta _{2}-\beta _{5}+\beta _{6}-\beta _{9})q^{3}+\cdots\)
575.4.b.i	$575$	$4$	575.b	5.b	$2$	$10$	$10$	$33.926$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None					115.4.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{6})q^{2}+(-\beta _{1}-\beta _{6}+\beta _{8}-\beta _{9})q^{3}+\cdots\)
575.4.b.j	$575$	$4$	575.b	5.b	$2$	$14$	$14$	$33.926$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓			575.4.a.l	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{6}-\beta _{8})q^{3}+(-4+\cdots)q^{4}+\cdots\)
575.4.b.k	$575$	$4$	575.b	5.b	$2$	$16$	$16$	$33.926$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					115.4.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{9})q^{2}+\beta _{6}q^{3}+(-5+\beta _{4}+\cdots)q^{4}+\cdots\)
575.4.b.l	$575$	$4$	575.b	5.b	$2$	$26$	$26$	$33.926$		None		✓	✓		575.4.a.o	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(575, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(575, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)