Space of modular forms of level 3751, weight 2, and Character 3751.bz

• Label: 3751.2.bz
• Level: $3751$
• Weight: $2$
• Character orbit: 3751.bz
• Rep. character: $\chi_{3751}(602,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $2240$
• Sturm bound: $704$

Defining parameters

Level:	\( N \)	\(=\)	\( 3751 = 11^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3751.bz (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 341 \)
Character field:			\(\Q(\zeta_{30})\)
Sturm bound:			\(704\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3751, [\chi])\).

	Total	New	Old
Modular forms	2912	2368	544
Cusp forms	2720	2240	480
Eisenstein series	192	128	64

Trace form

2240 * q + 10 * q^2 + 14 * q^3 + 546 * q^4 + 21 * q^5 + 5 * q^6 + 30 * q^7 + 10 * q^8 - 262 * q^9 + 10 * q^10 - 52 * q^12 + 15 * q^13 + 4 * q^14 - 518 * q^16 - 5 * q^17 - 10 * q^18 + 10 * q^19 + 9 * q^20 - 100 * q^21 - 95 * q^23 + 10 * q^24 + 303 * q^25 + 58 * q^26 - 40 * q^27 + 40 * q^28 + 10 * q^29 + 70 * q^30 - 39 * q^31 + 6 * q^34 + 25 * q^35 + 201 * q^36 - 4 * q^37 - 36 * q^38 - 60 * q^39 + 90 * q^40 + 70 * q^41 + q^42 - 10 * q^43 - 204 * q^45 + 100 * q^46 + 42 * q^47 + 21 * q^48 - 162 * q^49 - 45 * q^50 + 30 * q^51 - 60 * q^52 - 176 * q^53 + 90 * q^54 + 25 * q^56 + 55 * q^57 - 26 * q^59 + 30 * q^61 + 20 * q^62 + 15 * q^63 + 462 * q^64 - 5 * q^65 - 26 * q^67 - 5 * q^68 - 89 * q^69 - 72 * q^70 - 38 * q^71 - 405 * q^72 + 50 * q^73 - 250 * q^74 + 231 * q^75 - 70 * q^76 - 135 * q^78 - 10 * q^79 + 18 * q^80 + 202 * q^81 - 48 * q^82 + 60 * q^84 + 130 * q^85 + 51 * q^86 + 180 * q^87 - 80 * q^89 + 15 * q^90 + 240 * q^91 - 260 * q^92 + 202 * q^93 - 195 * q^95 - 130 * q^96 + 139 * q^97 + 30 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(3751, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3751, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3751, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(341, [\chi])\)\(^{\oplus 2}\)