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

• Label: 3751.2.e
• Level: $3751$
• Weight: $2$
• Character orbit: 3751.e
• Rep. character: $\chi_{3751}(1090,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $564$
• Sturm bound: $704$

Defining parameters

Level:	\( N \)	\(=\)	\( 3751 = 11^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3751.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(704\)

Dimensions

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

	Total	New	Old
Modular forms	728	600	128
Cusp forms	680	564	116
Eisenstein series	48	36	12

Trace form

564 * q + 4 * q^2 + 556 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^7 + 12 * q^8 - 266 * q^9 - 4 * q^12 - 4 * q^13 - 12 * q^15 + 532 * q^16 - 6 * q^17 - 14 * q^18 - 4 * q^19 + 8 * q^20 + 2 * q^21 - 40 * q^23 - 2 * q^24 - 248 * q^25 - 2 * q^26 + 36 * q^27 + 16 * q^28 + 8 * q^29 - 20 * q^30 - 8 * q^31 + 28 * q^32 + 24 * q^34 - 20 * q^35 - 270 * q^36 + 16 * q^38 + 16 * q^39 + 30 * q^40 + 14 * q^41 + 50 * q^42 + 18 * q^45 + 24 * q^46 - 20 * q^47 - 206 * q^49 - 32 * q^50 - 16 * q^51 - 18 * q^52 + 14 * q^53 + 24 * q^54 - 40 * q^56 - 8 * q^57 - 60 * q^58 + 10 * q^59 - 124 * q^60 + 32 * q^61 - 4 * q^62 + 8 * q^63 + 444 * q^64 - 18 * q^65 + 4 * q^67 - 16 * q^68 + 22 * q^69 - 184 * q^70 - 26 * q^71 + 32 * q^72 - 32 * q^73 - 18 * q^74 + 62 * q^75 - 14 * q^76 - 116 * q^78 - 12 * q^79 - 44 * q^80 - 222 * q^81 + 28 * q^82 - 34 * q^83 - 14 * q^84 + 56 * q^85 + 16 * q^86 + 34 * q^87 - 36 * q^89 - 50 * q^90 - 68 * q^91 + 16 * q^92 - 2 * q^93 - 52 * q^94 + 40 * q^95 + 12 * q^96 - 208 * q^97 - 68 * 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

\( S_{2}^{\mathrm{old}}(3751, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(341, [\chi])\)\(^{\oplus 2}\)