Space of modular forms of level 315, weight 5, and Character 315.n

• Label: 315.5.n
• Level: $315$
• Weight: $5$
• Character orbit: 315.n
• Rep. character: $\chi_{315}(62,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $128$
• Sturm bound: $240$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	315.n (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(315, [\chi])\).

	Total	New	Old
Modular forms	400	128	272
Cusp forms	368	128	240
Eisenstein series	32	0	32

Trace form

\( 128 q + 160 q^{7} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

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

Decomposition of \(S_{5}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(315, [\chi]) \cong \)