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

• Label: 3751.2.by
• Level: $3751$
• Weight: $2$
• Character orbit: 3751.by
• Rep. character: $\chi_{3751}(241,\cdot)$
• 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.by (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 + 14 * q^3 + 556 * q^4 + 6 * q^5 - 242 * q^9 - 82 * q^12 + 14 * q^14 - 20 * q^15 - 468 * q^16 + 4 * q^20 - 110 * q^23 - 1022 * q^25 + 78 * q^26 + 110 * q^27 + 46 * q^31 - 54 * q^34 - 984 * q^36 + 66 * q^37 + 114 * q^38 + 6 * q^42 - 224 * q^45 - 8 * q^47 - 134 * q^48 - 322 * q^49 + 44 * q^53 - 90 * q^56 + 60 * q^58 + 24 * q^59 - 390 * q^60 + 372 * q^64 - 26 * q^67 + 146 * q^69 + 28 * q^70 - 88 * q^71 + 16 * q^75 - 190 * q^78 + 488 * q^80 + 222 * q^81 + 2 * q^82 + 6 * q^86 - 120 * q^89 - 290 * q^91 + 182 * q^93 + 294 * q^97

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

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