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Properties

Label 315.5.cd
Level $315$
Weight $5$
Character orbit 315.cd
Rep. character $\chi_{315}(17,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $256$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 315.cd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(240\)

Dimensions

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

Total New Old
Modular forms 800 256 544
Cusp forms 736 256 480
Eisenstein series 64 0 64

Trace form

\( 256 q - 160 q^{7} + O(q^{10}) \) \( 256 q - 160 q^{7} - 384 q^{10} + 8192 q^{16} + 5120 q^{22} + 2176 q^{25} - 7360 q^{28} + 1280 q^{37} - 9480 q^{40} - 1360 q^{43} + 4080 q^{58} + 29328 q^{61} - 8320 q^{67} + 45752 q^{70} + 56520 q^{73} + 69000 q^{82} - 35920 q^{85} - 90480 q^{88} + 161040 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{5}^{\mathrm{old}}(315, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)