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Properties

Label 315.5.bw
Level $315$
Weight $5$
Character orbit 315.bw
Rep. character $\chi_{315}(47,\cdot)$
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.bw (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

\( 752 q - 6 q^{2} - 6 q^{3} - 12 q^{5} - 2 q^{7} + O(q^{10}) \) \( 752 q - 6 q^{2} - 6 q^{3} - 12 q^{5} - 2 q^{7} - 12 q^{10} - 6 q^{12} - 182 q^{15} + 22532 q^{16} + 1350 q^{17} + 1342 q^{18} - 1128 q^{21} + 60 q^{22} - 4 q^{25} + 3600 q^{27} + 472 q^{28} + 3220 q^{30} - 12 q^{31} - 11442 q^{32} - 1956 q^{33} + 4720 q^{36} - 4 q^{37} - 12 q^{38} - 8928 q^{41} - 3430 q^{42} - 4 q^{43} - 6144 q^{45} + 2104 q^{46} - 6 q^{47} - 954 q^{48} - 18444 q^{50} - 11836 q^{51} - 25968 q^{56} + 10016 q^{57} - 9476 q^{58} + 11330 q^{60} + 16692 q^{61} - 17472 q^{62} - 17766 q^{63} - 40614 q^{65} + 15540 q^{66} + 2 q^{67} - 86412 q^{68} + 4998 q^{70} - 422 q^{72} - 12 q^{73} - 6 q^{75} - 3072 q^{76} + 5754 q^{77} + 26590 q^{78} - 1536 q^{80} + 17480 q^{81} + 84 q^{82} - 4 q^{85} + 480 q^{87} + 14460 q^{88} - 43776 q^{90} - 16 q^{91} + 34644 q^{92} - 32576 q^{93} + 7494 q^{95} + 86004 q^{96} + 96 q^{98} + O(q^{100}) \)

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.