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Properties

Label 315.4.bs
Level $315$
Weight $4$
Character orbit 315.bs
Rep. character $\chi_{315}(52,\cdot)$
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.bs (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

\( 560 q - 4 q^{2} - 6 q^{3} - 6 q^{5} - 2 q^{7} + 16 q^{8} + O(q^{10}) \) \( 560 q - 4 q^{2} - 6 q^{3} - 6 q^{5} - 2 q^{7} + 16 q^{8} - 12 q^{10} + 12 q^{11} - 54 q^{12} - 92 q^{15} - 8200 q^{16} + 132 q^{17} + 46 q^{18} + 768 q^{20} - 384 q^{21} - 36 q^{22} - 102 q^{23} + 2 q^{25} - 24 q^{26} + 828 q^{27} + 136 q^{28} - 914 q^{30} + 1044 q^{32} - 6 q^{33} - 584 q^{35} + 400 q^{36} - 4 q^{37} - 6 q^{38} - 6 q^{40} + 1236 q^{41} + 296 q^{42} - 4 q^{43} + 1386 q^{45} + 496 q^{46} + 270 q^{48} - 1468 q^{50} + 884 q^{51} + 762 q^{52} + 556 q^{53} - 556 q^{56} + 2828 q^{57} - 470 q^{58} - 334 q^{60} + 1308 q^{63} + 1388 q^{65} - 12 q^{66} - 4 q^{67} - 2214 q^{68} + 498 q^{70} - 2368 q^{71} + 5206 q^{72} - 12 q^{73} + 3546 q^{75} + 768 q^{76} + 2426 q^{77} + 4810 q^{78} + 372 q^{80} + 3476 q^{81} - 60 q^{82} + 168 q^{83} - 4 q^{85} + 872 q^{86} + 3630 q^{87} + 1314 q^{88} + 5976 q^{90} - 16 q^{91} - 980 q^{92} + 622 q^{93} + 100 q^{95} - 8736 q^{96} - 4260 q^{98} + O(q^{100}) \)

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.