Space of modular forms of level 309, weight 5, and Character 309.j

• Label: 309.5.j
• Level: $309$
• Weight: $5$
• Character orbit: 309.j
• Rep. character: $\chi_{309}(10,\cdot)$
• Character field: $\Q(\zeta_{34})$
• Dimension: $1120$
• Sturm bound: $173$

Defining parameters

Level:	\( N \)	\(=\)	\( 309 = 3 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	309.j (of order \(34\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 103 \)
Character field:			\(\Q(\zeta_{34})\)
Sturm bound:			\(173\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(309, [\chi])\).

	Total	New	Old
Modular forms	2240	1120	1120
Cusp forms	2176	1120	1056
Eisenstein series	64	0	64

Trace form

\( 1120 q - 576 q^{4} + 56 q^{7} + 180 q^{8} + 1890 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(309, [\chi])\) into newform subspaces

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

Decomposition of \(S_{5}^{\mathrm{old}}(309, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(309, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(103, [\chi])\)\(^{\oplus 2}\)