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

• Label: 1638.2.l
• Level: $1638$
• Weight: $2$
• Character orbit: 1638.l
• Rep. character: $\chi_{1638}(373,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $224$
• Sturm bound: $672$

Defining parameters

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.l (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 819 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(672\)

Dimensions

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

	Total	New	Old
Modular forms	688	224	464
Cusp forms	656	224	432
Eisenstein series	32	0	32

Trace form

224 * q - 112 * q^4 - 4 * q^7 - 8 * q^9 + 8 * q^11 + 2 * q^13 - 4 * q^15 - 112 * q^16 - 16 * q^17 + 12 * q^18 - 8 * q^19 - 8 * q^21 + 8 * q^23 - 112 * q^25 - 4 * q^26 + 6 * q^27 + 8 * q^28 - 16 * q^29 - 8 * q^30 + 4 * q^31 + 16 * q^33 + 26 * q^35 + 4 * q^36 - 2 * q^37 - 24 * q^38 + 10 * q^39 + 4 * q^42 - 2 * q^43 + 8 * q^44 + 20 * q^45 - 12 * q^47 - 4 * q^49 - 4 * q^50 - 28 * q^51 - 4 * q^52 - 16 * q^53 - 6 * q^54 + 4 * q^57 + 20 * q^60 - 14 * q^61 - 38 * q^62 - 10 * q^63 + 224 * q^64 - 6 * q^65 - 14 * q^67 + 32 * q^68 + 24 * q^69 + 4 * q^71 - 12 * q^72 + 28 * q^73 - 12 * q^74 + 4 * q^75 + 4 * q^76 + 12 * q^77 - 4 * q^78 + 28 * q^79 + 4 * q^81 - 28 * q^83 + 16 * q^84 + 24 * q^85 - 8 * q^86 - 4 * q^87 + 10 * q^89 + 6 * q^90 + 26 * q^91 - 4 * q^92 + 20 * q^93 + 40 * q^95 - 2 * q^97 - 4 * 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

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