Space of modular forms of level 925, weight 2, and Character 925.bs

• Label: 925.2.bs
• Level: $925$
• Weight: $2$
• Character orbit: 925.bs
• Rep. character: $\chi_{925}(16,\cdot)$
• Character field: $\Q(\zeta_{45})$
• Dimension: $2208$
• Newform subspaces: $1$
• Sturm bound: $190$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.bs (of order \(45\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 925 \)
Character field:			\(\Q(\zeta_{45})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(190\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(925, [\chi])\).

	Total	New	Old
Modular forms	2304	2304	0
Cusp forms	2208	2208	0
Eisenstein series	96	96	0

Trace form

2208 * q - 18 * q^2 - 24 * q^3 - 18 * q^4 - 30 * q^5 - 36 * q^6 - 48 * q^7 - 27 * q^8 - 24 * q^9 - 12 * q^10 - 33 * q^11 + 42 * q^12 - 18 * q^13 - 9 * q^14 - 39 * q^15 - 30 * q^16 - 42 * q^17 - 54 * q^18 - 18 * q^19 + 72 * q^20 - 18 * q^21 - 30 * q^22 - 9 * q^23 - 60 * q^24 - 18 * q^25 + 138 * q^26 + 15 * q^27 - 30 * q^28 - 9 * q^29 - 120 * q^30 + 36 * q^31 - 72 * q^32 - 42 * q^33 + 27 * q^34 - 36 * q^35 - 444 * q^36 - 42 * q^37 - 120 * q^38 - 18 * q^39 - 27 * q^40 - 108 * q^41 - 228 * q^42 - 96 * q^43 + 21 * q^44 + 189 * q^45 - 162 * q^46 - 9 * q^47 - 21 * q^48 - 48 * q^49 + 78 * q^50 - 24 * q^51 + 90 * q^52 - 96 * q^53 + 42 * q^54 + 3 * q^55 + 21 * q^56 + 168 * q^57 - 90 * q^58 - 18 * q^59 - 150 * q^60 + 138 * q^61 + 36 * q^62 - 9 * q^63 + 183 * q^64 + 111 * q^65 + 27 * q^66 + 45 * q^67 - 96 * q^68 - 126 * q^69 + 141 * q^70 - 12 * q^71 + 156 * q^72 - 156 * q^73 - 90 * q^74 + 204 * q^75 - 24 * q^76 + 123 * q^77 + 9 * q^78 - 18 * q^79 - 24 * q^80 - 87 * q^81 - 24 * q^82 - 6 * q^83 + 27 * q^84 - 168 * q^85 - 54 * q^86 - 348 * q^87 - 33 * q^88 - 228 * q^89 - 213 * q^90 + 18 * q^91 - 228 * q^92 + 240 * q^93 - 30 * q^94 - 51 * q^95 - 174 * q^96 + 69 * q^97 - 45 * q^98 - 42 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(925, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
925.2.bs.a	$925$	$2$	925.bs	925.as	$45$	$2208$	$92$	$7.386$		None		✓	✓	✓	925.2.bs.a	$4$	$0$	\(-18\)	\(-24\)	\(-30\)	\(-48\)		$\mathrm{SU}(2)[C_{45}]$