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

• Label: 1400.2.n
• Level: $1400$
• Weight: $2$
• Character orbit: 1400.n
• Rep. character: $\chi_{1400}(699,\cdot)$
• Character field: $\Q$
• Dimension: $140$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1400.n (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 280 \)
Character field:			\(\Q\)
Sturm bound:			\(480\)

Dimensions

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

	Total	New	Old
Modular forms	252	148	104
Cusp forms	228	140	88
Eisenstein series	24	8	16

Trace form

\( 140 q + 4 q^{4} + 140 q^{9} - 8 q^{11} + 12 q^{16} + 12 q^{36} - 2 q^{44} - 42 q^{46} + 4 q^{49} + 16 q^{51} - 26 q^{56} + 94 q^{64} + 14 q^{74} + 156 q^{81} + 68 q^{84} - 114 q^{86} - 64 q^{91} + 56 q^{99}+O(q^{100}) \)

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

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