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Properties

Label 315.5.bt
Level $315$
Weight $5$
Character orbit 315.bt
Rep. character $\chi_{315}(58,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $752$
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.bt (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
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 784 784 0
Cusp forms 752 752 0
Eisenstein series 32 32 0

Trace form

\( 752 q - 4 q^{2} - 2 q^{3} + 2 q^{5} - 144 q^{6} - 2 q^{7} + 48 q^{8} + O(q^{10}) \) \( 752 q - 4 q^{2} - 2 q^{3} + 2 q^{5} - 144 q^{6} - 2 q^{7} + 48 q^{8} - 4 q^{10} - 152 q^{11} + 614 q^{12} - 4 q^{13} + 166 q^{15} - 45064 q^{16} - 454 q^{17} - 514 q^{18} + 1020 q^{20} - 1624 q^{21} - 68 q^{22} - 478 q^{23} + 2 q^{25} - 8 q^{26} - 788 q^{27} + 536 q^{28} - 794 q^{30} - 8 q^{31} - 5836 q^{32} + 1622 q^{33} - 6092 q^{35} + 368 q^{36} - 4 q^{37} + 66 q^{38} + 1026 q^{40} + 2968 q^{41} + 3488 q^{42} - 4 q^{43} - 3146 q^{45} - 2120 q^{46} - 4 q^{47} - 9994 q^{48} + 692 q^{50} - 13216 q^{51} + 962 q^{52} + 4496 q^{53} - 2516 q^{55} + 16788 q^{56} + 19928 q^{57} + 4866 q^{58} - 21830 q^{60} - 11144 q^{61} + 5680 q^{62} + 27770 q^{63} - 27076 q^{65} - 22172 q^{66} - 4 q^{67} + 15490 q^{68} - 2502 q^{70} + 736 q^{71} - 18154 q^{72} - 4 q^{73} - 13074 q^{75} - 1032 q^{76} + 20402 q^{77} + 25242 q^{78} - 3016 q^{80} - 9064 q^{81} + 28 q^{82} + 21416 q^{83} - 4 q^{85} + 39496 q^{86} + 39404 q^{87} + 9282 q^{88} - 48012 q^{90} - 16 q^{91} - 10468 q^{92} + 38650 q^{93} + 57780 q^{95} - 24192 q^{96} - 4 q^{97} - 32556 q^{98} + O(q^{100}) \)

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.