Space of modular forms of level 1400, weight 2, and Character 1400.cl

• Label: 1400.2.cl
• Level: $1400$
• Weight: $2$
• Character orbit: 1400.cl
• Rep. character: $\chi_{1400}(157,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $560$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1400.cl (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 280 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1400, [\chi])\).

	Total	New	Old
Modular forms	1008	592	416
Cusp forms	912	560	352
Eisenstein series	96	32	64

Trace form

560 * q + 2 * q^2 + 8 * q^7 - 4 * q^8 + 6 * q^12 + 12 * q^16 + 12 * q^17 + 16 * q^18 + 16 * q^22 + 4 * q^23 - 12 * q^26 + 50 * q^28 - 24 * q^31 - 18 * q^32 + 12 * q^33 - 48 * q^36 + 24 * q^38 + 10 * q^42 - 16 * q^46 + 84 * q^47 - 72 * q^52 + 16 * q^56 + 40 * q^57 - 2 * q^58 + 24 * q^63 + 60 * q^66 - 60 * q^68 - 160 * q^71 - 52 * q^72 + 12 * q^73 + 24 * q^78 + 240 * q^81 + 54 * q^82 + 72 * q^86 + 48 * q^87 - 60 * q^88 - 12 * q^92 + 156 * q^96 + 130 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(1400, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1400, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1400, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)