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Properties

Label 315.4.bv
Level $315$
Weight $4$
Character orbit 315.bv
Rep. character $\chi_{315}(23,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $560$
Sturm bound $192$

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Defining parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 315.bv (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(315, [\chi])\).

Total New Old
Modular forms 592 592 0
Cusp forms 560 560 0
Eisenstein series 32 32 0

Trace form

\( 560 q - 2 q^{3} - 6 q^{5} - 2 q^{7} + O(q^{10}) \) \( 560 q - 2 q^{3} - 6 q^{5} - 2 q^{7} - 4 q^{10} + 12 q^{11} + 230 q^{12} - 4 q^{13} + 76 q^{15} - 8200 q^{16} - 144 q^{17} - 82 q^{18} - 12 q^{20} + 368 q^{21} + 28 q^{22} - 318 q^{23} + 2 q^{25} + 4 q^{27} + 104 q^{28} - 1250 q^{30} - 8 q^{31} + 530 q^{33} + 1424 q^{36} - 4 q^{37} - 102 q^{38} + 258 q^{40} - 1260 q^{41} - 520 q^{42} - 4 q^{43} - 878 q^{45} - 512 q^{46} + 1778 q^{48} - 684 q^{50} - 892 q^{51} + 290 q^{52} + 484 q^{55} + 3156 q^{56} + 68 q^{57} - 534 q^{58} - 3638 q^{60} + 64 q^{61} + 2468 q^{63} - 2684 q^{66} - 4 q^{67} - 1542 q^{68} + 498 q^{70} - 4186 q^{72} - 4 q^{73} + 4086 q^{75} - 264 q^{76} + 3258 q^{77} + 654 q^{78} - 1116 q^{80} + 3476 q^{81} - 20 q^{82} - 12 q^{83} - 4 q^{85} + 8304 q^{86} + 110 q^{87} - 798 q^{88} - 1524 q^{90} - 16 q^{91} + 3780 q^{92} + 3886 q^{93} - 2976 q^{96} - 4 q^{97} - 48 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

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