Space of modular forms of level 175, weight 4, and Character 175.b

• Label: 175.4.b
• Level: $175$
• Weight: $4$
• Character orbit: 175.b
• Rep. character: $\chi_{175}(99,\cdot)$
• Character field: $\Q$
• Dimension: $26$
• Newform subspaces: $6$
• Sturm bound: $80$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(80\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(175, [\chi])\).

	Total	New	Old
Modular forms	66	26	40
Cusp forms	54	26	28
Eisenstein series	12	0	12

Trace form

26 * q - 120 * q^4 - 24 * q^6 - 294 * q^9 - 80 * q^11 + 56 * q^14 + 392 * q^16 - 96 * q^19 - 196 * q^21 - 116 * q^24 + 452 * q^26 + 276 * q^29 - 168 * q^31 - 1328 * q^34 + 2196 * q^36 - 560 * q^39 + 1568 * q^41 + 2726 * q^44 - 1526 * q^46 - 1274 * q^49 - 4036 * q^51 + 3868 * q^54 - 714 * q^56 - 92 * q^59 + 3664 * q^61 + 1314 * q^64 - 2500 * q^66 - 3048 * q^69 - 3588 * q^71 - 8318 * q^74 + 1596 * q^76 + 5300 * q^79 + 1522 * q^81 + 2800 * q^84 + 2486 * q^86 - 1984 * q^89 - 224 * q^91 + 7108 * q^94 - 13428 * q^96 - 52 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(175, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
175.4.b.a	$175$	$4$	175.b	5.b	$2$	$2$	$2$	$10.325$	\(\Q(\sqrt{-1}) \)	None					35.4.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+8 i q^{3}+7 q^{4}-8 q^{6}+7 i q^{7}+\cdots\)
175.4.b.b	$175$	$4$	175.b	5.b	$2$	$2$	$2$	$10.325$	\(\Q(\sqrt{-1}) \)	None					7.4.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-2 i q^{3}+7 q^{4}+2 q^{6}+7 i q^{7}+\cdots\)
175.4.b.c	$175$	$4$	175.b	5.b	$2$	$4$	$4$	$10.325$	\(\Q(\zeta_{8})\)	None					35.4.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{2}+4\beta_1)q^{2}+(-4\beta_{2}-\beta_1)q^{3}+\cdots\)
175.4.b.d	$175$	$4$	175.b	5.b	$2$	$4$	$4$	$10.325$	\(\Q(i, \sqrt{41})\)	None		✓			175.4.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}-2\beta _{2})q^{3}+(-3+\beta _{3})q^{4}+\cdots\)
175.4.b.e	$175$	$4$	175.b	5.b	$2$	$6$	$6$	$10.325$	6.0.3299353600.1	None					35.4.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{2})q^{2}+(-\beta _{1}+\beta _{2}+\beta _{5})q^{3}+\cdots\)
175.4.b.f	$175$	$4$	175.b	5.b	$2$	$8$	$8$	$10.325$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓	✓		175.4.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{2})q^{2}+(-\beta _{2}-\beta _{5})q^{3}+(-9+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(175, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(175, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)