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Properties

Label 315.4.bx
Level $315$
Weight $4$
Character orbit 315.bx
Rep. character $\chi_{315}(2,\cdot)$
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.bx (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

\( 560 q - 6 q^{2} - 2 q^{3} - 2 q^{7} + O(q^{10}) \) \( 560 q - 6 q^{2} - 2 q^{3} - 2 q^{7} - 4 q^{10} - 142 q^{12} - 4 q^{13} + 76 q^{15} + 4100 q^{16} + 144 q^{17} + 62 q^{18} - 12 q^{20} - 244 q^{21} + 28 q^{22} - 4 q^{25} + 4 q^{27} + 104 q^{28} + 1240 q^{30} + 4 q^{31} + 990 q^{32} - 106 q^{33} + 1424 q^{36} - 4 q^{37} - 516 q^{40} - 1260 q^{41} - 406 q^{42} - 4 q^{43} + 382 q^{45} - 512 q^{46} - 6 q^{47} + 1778 q^{48} - 684 q^{50} + 1148 q^{51} - 580 q^{52} + 484 q^{55} + 3936 q^{56} + 68 q^{57} + 1068 q^{58} - 854 q^{60} - 32 q^{61} - 4714 q^{63} + 2082 q^{65} + 2764 q^{66} + 2 q^{67} - 1002 q^{70} + 818 q^{72} - 4 q^{73} + 534 q^{75} - 264 q^{76} + 3210 q^{77} + 654 q^{78} + 1116 q^{80} - 2992 q^{81} - 20 q^{82} - 12 q^{83} - 4 q^{85} + 3584 q^{87} + 1596 q^{88} - 1524 q^{90} - 16 q^{91} + 3780 q^{92} - 1382 q^{93} - 1506 q^{95} - 5364 q^{96} - 4 q^{97} + 48 q^{98} + O(q^{100}) \)

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.