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Properties

Label 315.4.k
Level $315$
Weight $4$
Character orbit 315.k
Rep. character $\chi_{315}(16,\cdot)$
Character field $\Q(\zeta_{3})$
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.k (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
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

\( 192 q - 384 q^{4} - 40 q^{5} + 8 q^{6} + 12 q^{7} + 30 q^{9} + O(q^{10}) \) \( 192 q - 384 q^{4} - 40 q^{5} + 8 q^{6} + 12 q^{7} + 30 q^{9} + 8 q^{11} + 220 q^{12} + 24 q^{13} + 144 q^{14} - 20 q^{15} - 1536 q^{16} + 272 q^{17} - 252 q^{18} - 120 q^{19} + 240 q^{20} - 130 q^{21} - 168 q^{23} - 548 q^{24} + 4800 q^{25} - 80 q^{26} - 12 q^{27} + 192 q^{28} - 250 q^{29} - 280 q^{30} - 120 q^{31} + 980 q^{32} + 56 q^{33} + 1320 q^{36} + 168 q^{37} - 2984 q^{38} + 1352 q^{39} + 274 q^{41} - 636 q^{42} + 168 q^{43} + 706 q^{44} + 330 q^{45} + 252 q^{46} + 2012 q^{47} + 92 q^{48} + 156 q^{49} + 2588 q^{51} - 768 q^{52} - 1080 q^{53} - 480 q^{54} - 114 q^{56} - 1072 q^{57} + 500 q^{59} + 150 q^{60} - 858 q^{61} - 5640 q^{62} - 856 q^{63} + 12288 q^{64} + 320 q^{65} - 6032 q^{66} - 588 q^{67} - 3388 q^{68} + 48 q^{69} + 180 q^{70} - 1968 q^{71} - 952 q^{72} + 672 q^{73} + 4928 q^{74} - 1920 q^{76} - 176 q^{77} + 712 q^{78} - 48 q^{79} + 2240 q^{80} - 2494 q^{81} + 2764 q^{83} + 8472 q^{84} - 360 q^{85} - 3076 q^{86} - 4396 q^{87} + 742 q^{89} - 1170 q^{90} - 1740 q^{91} - 700 q^{92} - 4224 q^{93} + 1224 q^{94} + 3970 q^{96} + 528 q^{97} - 11494 q^{98} + 6780 q^{99} + O(q^{100}) \)

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.

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

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