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Properties

Label 315.4.cb
Level $315$
Weight $4$
Character orbit 315.cb
Rep. character $\chi_{315}(13,\cdot)$
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.cb (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

\( 560 q - 4 q^{2} - 2 q^{7} - 80 q^{8} + O(q^{10}) \) \( 560 q - 4 q^{2} - 2 q^{7} - 80 q^{8} + 160 q^{15} + 4088 q^{16} - 56 q^{18} - 384 q^{21} + 60 q^{22} - 108 q^{23} - 4 q^{25} - 296 q^{28} - 416 q^{30} - 144 q^{32} + 1072 q^{35} - 2384 q^{36} - 16 q^{37} - 1318 q^{42} - 4 q^{43} + 1984 q^{46} - 796 q^{50} + 248 q^{51} + 2224 q^{53} + 1856 q^{56} - 1864 q^{57} + 940 q^{58} + 80 q^{60} - 4134 q^{63} - 700 q^{65} - 4 q^{67} + 498 q^{70} - 2368 q^{71} + 2308 q^{72} - 790 q^{77} - 3692 q^{78} + 5960 q^{81} - 4 q^{85} - 1744 q^{86} - 2532 q^{88} - 16 q^{91} - 1796 q^{92} - 5252 q^{93} - 1400 q^{95} - 432 q^{98} + O(q^{100}) \)

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.