Properties

Label 312.6.j
Level $312$
Weight $6$
Character orbit 312.j
Rep. character $\chi_{312}(131,\cdot)$
Character field $\Q$
Dimension $240$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 312.j (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(312, [\chi])\).

Total New Old
Modular forms 284 240 44
Cusp forms 276 240 36
Eisenstein series 8 0 8

Trace form

\( 240 q + 20 q^{4} - 184 q^{10} - 1090 q^{12} - 848 q^{16} - 216 q^{18} + 4720 q^{19} - 7260 q^{22} - 2876 q^{24} + 150000 q^{25} + 26112 q^{28} - 31746 q^{30} - 5672 q^{33} - 3416 q^{34} + 3690 q^{36} - 1480 q^{40}+ \cdots + 132176 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(312, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(312, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(312, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)