Properties

Label 315.4.t
Level $315$
Weight $4$
Character orbit 315.t
Rep. character $\chi_{315}(101,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $192$
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.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(315, [\chi])\).

Total New Old
Modular forms 296 192 104
Cusp forms 280 192 88
Eisenstein series 16 0 16

Trace form

\( 192 q - 768 q^{4} - 12 q^{7} + 44 q^{9} + O(q^{10}) \) \( 192 q - 768 q^{4} - 12 q^{7} + 44 q^{9} - 12 q^{11} - 330 q^{12} + 72 q^{13} + 18 q^{14} - 20 q^{15} + 3072 q^{16} + 154 q^{18} + 144 q^{21} + 252 q^{23} - 2400 q^{25} + 240 q^{26} - 36 q^{27} + 192 q^{28} + 126 q^{29} + 140 q^{30} - 1992 q^{36} - 168 q^{37} + 1740 q^{38} - 72 q^{39} - 618 q^{41} + 396 q^{42} - 168 q^{43} - 2118 q^{44} - 990 q^{45} - 252 q^{46} + 792 q^{47} + 2640 q^{48} - 42 q^{49} + 348 q^{51} - 1152 q^{52} - 1128 q^{53} + 2586 q^{54} + 384 q^{56} + 48 q^{57} - 3000 q^{59} - 660 q^{60} + 3308 q^{63} - 12288 q^{64} + 900 q^{66} + 1176 q^{67} - 4710 q^{68} - 360 q^{70} + 938 q^{72} - 2940 q^{74} + 5616 q^{77} + 5448 q^{78} - 1776 q^{79} + 4940 q^{81} - 3660 q^{83} - 7812 q^{84} + 360 q^{85} + 1758 q^{86} - 396 q^{87} - 2226 q^{89} - 3510 q^{90} + 900 q^{91} - 12012 q^{92} - 864 q^{93} - 3066 q^{96} + 1584 q^{97} - 11286 q^{98} - 4532 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(315, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)