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Properties

Label 315.10.bz
Level $315$
Weight $10$
Character orbit 315.bz
Rep. character $\chi_{315}(73,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $712$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 315.bz (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(315, [\chi])\).

Total New Old
Modular forms 1760 728 1032
Cusp forms 1696 712 984
Eisenstein series 64 16 48

Trace form

\( 712 q + 2 q^{2} - 1698 q^{5} - 13572 q^{7} + 628 q^{8} + O(q^{10}) \) \( 712 q + 2 q^{2} - 1698 q^{5} - 13572 q^{7} + 628 q^{8} - 153798 q^{10} - 26096 q^{11} + 22007172 q^{16} + 1578678 q^{17} - 2128008 q^{22} - 5311142 q^{23} - 1461706 q^{25} + 2294604 q^{26} - 20603030 q^{28} + 8900220 q^{31} - 16423146 q^{32} + 1952664 q^{35} - 12375026 q^{37} - 20958660 q^{38} - 89260962 q^{40} + 4009072 q^{43} + 2421124 q^{46} + 147698766 q^{47} - 350932780 q^{50} - 126665976 q^{52} - 208887686 q^{53} + 444503996 q^{56} + 130611606 q^{58} + 429110448 q^{61} - 50642882 q^{65} + 315475178 q^{67} + 408371100 q^{68} - 2051911728 q^{70} - 1175832080 q^{71} - 516971382 q^{73} - 264928990 q^{77} - 3775239504 q^{80} + 3707550078 q^{82} - 2869623792 q^{85} + 2815202248 q^{86} + 21295996 q^{88} + 2561145640 q^{91} + 11233897052 q^{92} - 279877586 q^{95} - 11494866 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{10}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)