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

• Label: 175.4.t
• Level: $175$
• Weight: $4$
• Character orbit: 175.t
• Rep. character: $\chi_{175}(4,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $464$
• Newform subspaces: $1$
• Sturm bound: $80$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.t (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 175 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(80\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	496	496	0
Cusp forms	464	464	0
Eisenstein series	32	32	0

Trace form

464 * q - 5 * q^2 - 5 * q^3 - 227 * q^4 - 8 * q^5 + 68 * q^6 + 190 * q^8 - 489 * q^9 + 27 * q^10 + 39 * q^11 - 5 * q^12 - 20 * q^13 - 96 * q^14 - 314 * q^15 + 813 * q^16 + 315 * q^17 + 149 * q^19 - 604 * q^20 - 63 * q^21 + 700 * q^22 - 365 * q^23 - 1054 * q^24 + 182 * q^25 + 1224 * q^26 + 1300 * q^27 - 690 * q^28 + 36 * q^29 - 67 * q^30 + 39 * q^31 - 805 * q^33 - 236 * q^34 - 866 * q^35 - 4324 * q^36 - 5 * q^37 - 1250 * q^38 + 535 * q^39 - 679 * q^40 + 1588 * q^41 + 1130 * q^42 + 173 * q^44 + 1095 * q^45 - 199 * q^46 - 5 * q^47 + 60 * q^48 - 388 * q^49 - 1874 * q^50 - 488 * q^51 + 2310 * q^52 - 2165 * q^53 + 1115 * q^54 + 722 * q^55 + 590 * q^56 + 3415 * q^58 + 921 * q^59 + 5769 * q^60 - 1063 * q^61 + 8380 * q^62 - 725 * q^63 + 6342 * q^64 + 941 * q^65 - 1193 * q^66 + 2305 * q^67 - 3960 * q^69 - 9555 * q^70 - 2048 * q^71 - 5100 * q^72 - 2285 * q^73 - 1470 * q^74 + 1772 * q^75 - 15476 * q^76 - 4445 * q^77 + 250 * q^78 - 251 * q^79 - 9054 * q^80 + 3557 * q^81 + 6760 * q^83 - 4179 * q^84 + 5582 * q^85 + 2633 * q^86 - 5 * q^87 + 6630 * q^88 + 93 * q^89 + 20976 * q^90 + 1776 * q^91 - 710 * q^92 + 1629 * q^94 - 2950 * q^95 + 793 * q^96 - 13040 * q^97 + 16890 * q^98 - 7728 * 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.t.a	$175$	$4$	175.t	175.t	$30$	$464$	$58$	$10.325$		None		✓	✓	✓	175.4.t.a	$4$	$0$	\(-5\)	\(-5\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{30}]$