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

• Label: 3751.2.h
• Level: $3751$
• Weight: $2$
• Character orbit: 3751.h
• Rep. character: $\chi_{3751}(807,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $1080$
• Sturm bound: $704$

Defining parameters

Level:	\( N \)	\(=\)	\( 3751 = 11^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3751.h (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
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	1080	376
Cusp forms	1360	1080	280
Eisenstein series	96	0	96

Trace form

1080 * q + 6 * q^2 + 4 * q^3 - 266 * q^4 + 4 * q^5 - 6 * q^6 - 2 * q^7 - 2 * q^8 - 270 * q^9 + 28 * q^12 + 8 * q^13 - 18 * q^14 - 4 * q^15 - 286 * q^16 + 6 * q^17 - 30 * q^18 + 6 * q^19 + 16 * q^20 + 8 * q^21 + 24 * q^23 - 22 * q^24 - 278 * q^25 + 40 * q^26 - 2 * q^27 + 18 * q^28 + 6 * q^29 + 8 * q^30 - 48 * q^32 - 28 * q^34 - 26 * q^35 - 268 * q^36 - 8 * q^37 + 44 * q^38 - 22 * q^39 + 60 * q^40 + 8 * q^41 + 112 * q^42 + 40 * q^43 + 72 * q^45 + 18 * q^46 + 24 * q^47 + 52 * q^48 - 296 * q^49 + 74 * q^50 - 26 * q^51 - 16 * q^52 - 14 * q^53 - 88 * q^54 - 100 * q^56 - 30 * q^57 + 30 * q^58 - 24 * q^59 + 32 * q^60 - 14 * q^61 + 8 * q^62 + 6 * q^63 - 274 * q^64 + 44 * q^65 - 60 * q^67 + 4 * q^68 + 2 * q^69 + 8 * q^70 + 8 * q^71 + 40 * q^72 + 50 * q^73 + 40 * q^74 - 70 * q^75 - 68 * q^76 - 312 * q^78 - 38 * q^79 - 68 * q^80 - 332 * q^81 + 46 * q^82 - 2 * q^83 + 58 * q^85 - 22 * q^86 - 96 * q^87 + 36 * q^89 - 48 * q^90 - 20 * q^91 + 128 * q^92 + 92 * q^94 + 102 * q^95 + 88 * q^96 - 10 * q^97 + 64 * 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

\( S_{2}^{\mathrm{old}}(3751, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(341, [\chi])\)\(^{\oplus 2}\)