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Properties

Label 315.5.bu
Level $315$
Weight $5$
Character orbit 315.bu
Rep. character $\chi_{315}(38,\cdot)$
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.bu (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

\( 752 q - 6 q^{3} - 6 q^{5} - 2 q^{7} + O(q^{10}) \) \( 752 q - 6 q^{3} - 6 q^{5} - 2 q^{7} - 12 q^{10} - 480 q^{11} + 90 q^{12} - 182 q^{15} - 45064 q^{16} - 1350 q^{17} - 770 q^{18} + 1608 q^{21} + 60 q^{22} - 1446 q^{23} + 2 q^{25} - 3600 q^{27} + 472 q^{28} + 3430 q^{30} - 6 q^{33} + 4720 q^{36} - 4 q^{37} - 6 q^{38} - 6 q^{40} + 8928 q^{41} - 2848 q^{42} - 4 q^{43} + 14202 q^{45} + 2104 q^{46} - 12 q^{47} + 954 q^{48} - 18444 q^{50} + 13208 q^{51} + 3066 q^{52} - 13836 q^{56} + 10016 q^{57} + 4738 q^{58} - 17086 q^{60} + 17472 q^{62} + 26670 q^{63} - 12 q^{66} - 4 q^{67} - 43206 q^{68} - 2502 q^{70} + 22246 q^{72} - 12 q^{73} + 7146 q^{75} + 3072 q^{76} - 20886 q^{77} + 26590 q^{78} + 1536 q^{80} - 9064 q^{81} + 84 q^{82} - 4 q^{85} + 52800 q^{86} - 35196 q^{87} - 7230 q^{88} + 43776 q^{90} - 16 q^{91} + 34644 q^{92} + 7306 q^{93} + 9552 q^{96} - 96 q^{98} + O(q^{100}) \)

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.