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Properties

Label 315.5.cf
Level $315$
Weight $5$
Character orbit 315.cf
Rep. character $\chi_{315}(83,\cdot)$
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.cf (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

\( 752 q - 12 q^{2} - 2 q^{7} + O(q^{10}) \) \( 752 q - 12 q^{2} - 2 q^{7} + 444 q^{11} + 340 q^{15} + 22520 q^{16} - 584 q^{18} + 1608 q^{21} - 132 q^{22} + 1428 q^{23} - 4 q^{25} - 968 q^{28} + 9760 q^{30} + 6816 q^{32} - 2960 q^{36} - 16 q^{37} + 4250 q^{42} - 4 q^{43} + 8416 q^{46} + 36852 q^{50} - 1396 q^{51} + 39768 q^{56} - 35896 q^{57} - 9476 q^{58} + 19760 q^{60} - 19416 q^{63} + 40596 q^{65} - 4 q^{67} - 2502 q^{70} - 71084 q^{72} + 15114 q^{77} + 8044 q^{78} - 34984 q^{81} - 4 q^{85} + 105600 q^{86} + 14268 q^{88} - 16 q^{91} + 34356 q^{92} - 42632 q^{93} - 7512 q^{95} + O(q^{100}) \)

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.