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

• Label: 3751.2.bj
• Level: $3751$
• Weight: $2$
• Character orbit: 3751.bj
• Rep. character: $\chi_{3751}(366,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $2240$
• Sturm bound: $704$

Defining parameters

Level:	\( N \)	\(=\)	\( 3751 = 11^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3751.bj (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 341 \)
Character field:			\(\Q(\zeta_{15})\)
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 + 12 * q^2 + 7 * q^3 - 532 * q^4 + q^5 + 3 * q^6 - q^7 - 4 * q^8 + 271 * q^9 + 12 * q^10 - 106 * q^12 + q^13 + 11 * q^14 + 68 * q^15 - 500 * q^16 - 3 * q^17 + 27 * q^18 + 3 * q^19 - 45 * q^20 - 26 * q^21 - 76 * q^23 + 7 * q^24 + 281 * q^25 + 58 * q^26 - 50 * q^27 + 9 * q^28 - 24 * q^29 - 38 * q^30 + 8 * q^31 + 24 * q^32 - 22 * q^34 + 44 * q^35 + 229 * q^36 + 13 * q^37 - 44 * q^38 - 8 * q^39 - 24 * q^40 + 4 * q^41 + 36 * q^42 - 28 * q^43 + 82 * q^45 + 12 * q^46 - 14 * q^47 + 86 * q^48 + 219 * q^49 - 71 * q^50 + 23 * q^51 + 34 * q^52 - 55 * q^53 + 172 * q^54 - 110 * q^56 + 15 * q^57 + q^59 - 126 * q^60 + 68 * q^61 - 11 * q^62 + 138 * q^63 - 412 * q^64 - 20 * q^65 - 12 * q^67 + 26 * q^68 - 90 * q^69 + 222 * q^70 - 35 * q^71 - 124 * q^72 - 5 * q^73 + 80 * q^74 - 65 * q^75 + 26 * q^76 - 184 * q^78 + 59 * q^79 + 138 * q^80 + 189 * q^81 + 73 * q^82 + 95 * q^83 + 111 * q^84 + 152 * q^85 + 55 * q^86 - 24 * q^87 - 360 * q^89 - 117 * q^90 + 70 * q^91 + 48 * q^92 - 50 * q^93 - 62 * q^94 + 12 * q^95 - 40 * q^96 + 150 * q^97 + 188 * 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

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