Space of modular forms of level 3762, weight 2, and Character 3762.i

• Label: 3762.2.i
• Level: $3762$
• Weight: $2$
• Character orbit: 3762.i
• Rep. character: $\chi_{3762}(1255,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $360$
• Sturm bound: $1440$

Defining parameters

Level:	\( N \)	\(=\)	\( 3762 = 2 \cdot 3^{2} \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3762.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3762, [\chi])\).

	Total	New	Old
Modular forms	1456	360	1096
Cusp forms	1424	360	1064
Eisenstein series	32	0	32

Trace form

360 * q - 4 * q^3 - 180 * q^4 - 4 * q^5 + 16 * q^6 - 12 * q^9 - 4 * q^11 - 4 * q^12 + 8 * q^14 + 4 * q^15 - 180 * q^16 - 4 * q^20 - 16 * q^21 - 8 * q^23 - 8 * q^24 - 168 * q^25 + 48 * q^26 - 16 * q^27 + 8 * q^29 + 40 * q^30 + 12 * q^31 + 8 * q^33 - 48 * q^35 + 24 * q^36 - 24 * q^37 - 12 * q^38 - 12 * q^39 + 8 * q^41 - 36 * q^42 + 8 * q^44 + 8 * q^45 - 48 * q^46 + 16 * q^47 + 8 * q^48 - 156 * q^49 - 24 * q^51 - 8 * q^53 + 16 * q^54 - 24 * q^55 + 8 * q^56 + 4 * q^59 - 8 * q^60 + 24 * q^61 - 48 * q^62 + 136 * q^63 + 360 * q^64 + 56 * q^65 + 12 * q^67 - 72 * q^69 + 24 * q^70 - 40 * q^71 + 12 * q^74 + 24 * q^75 - 16 * q^77 + 32 * q^78 + 8 * q^80 - 12 * q^81 + 96 * q^82 - 96 * q^83 + 8 * q^84 - 48 * q^85 - 28 * q^87 + 64 * q^89 - 24 * q^90 - 8 * q^92 - 84 * q^93 + 24 * q^94 - 8 * q^96 - 36 * q^97 - 20 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(3762, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3762, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3762, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1881, [\chi])\)\(^{\oplus 2}\)