Space of modular forms of level 1638, weight 2, and Character 1638.cs

• Label: 1638.2.cs
• Level: $1638$
• Weight: $2$
• Character orbit: 1638.cs
• Rep. character: $\chi_{1638}(589,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $168$
• Sturm bound: $672$

Defining parameters

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.cs (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1638, [\chi])\).

	Total	New	Old
Modular forms	688	168	520
Cusp forms	656	168	488
Eisenstein series	32	0	32

Trace form

168 * q - 168 * q^4 + 4 * q^9 - 8 * q^14 - 12 * q^15 + 168 * q^16 + 12 * q^18 - 12 * q^21 - 4 * q^23 + 84 * q^25 + 24 * q^27 + 88 * q^29 + 20 * q^30 - 8 * q^35 - 4 * q^36 + 12 * q^38 + 32 * q^39 - 48 * q^41 + 60 * q^45 - 60 * q^47 + 84 * q^49 - 12 * q^50 + 64 * q^51 + 48 * q^53 - 36 * q^54 + 8 * q^56 - 48 * q^57 + 12 * q^60 - 12 * q^62 - 168 * q^64 - 96 * q^65 + 16 * q^66 - 12 * q^69 - 12 * q^71 - 12 * q^72 - 56 * q^74 + 80 * q^75 + 16 * q^77 + 40 * q^78 + 12 * q^79 + 96 * q^81 + 24 * q^82 + 36 * q^83 + 12 * q^84 - 24 * q^86 + 100 * q^87 + 36 * q^89 - 8 * q^90 + 12 * q^91 + 4 * q^92 + 36 * q^93 + 48 * q^95 + 48 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1638, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1638, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1638, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(819, [\chi])\)\(^{\oplus 2}\)