Space of modular forms of level 350, weight 7, and Character 350.v

• Label: 350.7.v
• Level: $350$
• Weight: $7$
• Character orbit: 350.v
• Rep. character: $\chi_{350}(19,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $960$
• Sturm bound: $420$

Defining parameters

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	350.v (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 175 \)
Character field:			\(\Q(\zeta_{30})\)
Sturm bound:			\(420\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(350, [\chi])\).

	Total	New	Old
Modular forms	2912	960	1952
Cusp forms	2848	960	1888
Eisenstein series	64	0	64

Trace form

\( 960 q - 3840 q^{4} + 336 q^{5} + 29160 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(350, [\chi])\) into newform subspaces

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

Decomposition of \(S_{7}^{\mathrm{old}}(350, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(350, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)