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

• Label: 3751.2.g
• Level: $3751$
• Weight: $2$
• Character orbit: 3751.g
• Rep. character: $\chi_{3751}(729,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $1120$
• Sturm bound: $704$

Defining parameters

Level:	\( N \)	\(=\)	\( 3751 = 11^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3751.g (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 341 \)
Character field:			\(\Q(\zeta_{5})\)
Sturm bound:			\(704\)

Dimensions

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

	Total	New	Old
Modular forms	1456	1184	272
Cusp forms	1360	1120	240
Eisenstein series	96	64	32

Trace form

1120 * q + q^2 + 7 * q^3 - 271 * q^4 + 12 * q^5 + 4 * q^6 + 3 * q^7 - 7 * q^8 - 257 * q^9 + 10 * q^10 - 35 * q^12 + 28 * q^13 + 19 * q^14 - 19 * q^15 - 239 * q^16 - 4 * q^17 - 15 * q^18 + q^19 - 50 * q^20 + 23 * q^21 - 22 * q^23 - 47 * q^24 - 234 * q^25 - 77 * q^26 + 19 * q^27 - 17 * q^28 - 19 * q^29 - 22 * q^30 + 10 * q^31 + 62 * q^32 - 34 * q^34 - 16 * q^35 - 256 * q^36 - 7 * q^37 - 30 * q^38 + 23 * q^39 + 13 * q^41 + 34 * q^42 - 6 * q^45 + 78 * q^46 + 13 * q^47 - 98 * q^48 - 223 * q^49 + 4 * q^50 + 9 * q^51 - 26 * q^52 + 22 * q^53 - 98 * q^54 + 26 * q^56 - 10 * q^57 - 86 * q^58 - 51 * q^59 + 10 * q^60 - 24 * q^61 - 37 * q^62 + 21 * q^63 - 189 * q^64 - q^65 - 96 * q^67 + 64 * q^68 + 54 * q^69 + 50 * q^70 - 7 * q^71 + 80 * q^72 - 15 * q^73 + 134 * q^75 + 2 * q^76 + 93 * q^78 - 23 * q^79 + 61 * q^80 - 214 * q^81 - 63 * q^82 + 28 * q^83 + 120 * q^84 - 7 * q^85 + 60 * q^86 + 24 * q^87 - 20 * q^89 + 222 * q^90 - 105 * q^91 - 42 * q^92 + 167 * q^93 + 2 * q^94 + 82 * q^95 + 8 * q^96 + 6 * q^97 + 84 * 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

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