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Properties

Label 315.5.s
Level $315$
Weight $5$
Character orbit 315.s
Rep. character $\chi_{315}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $256$
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.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(315, [\chi])\).

Total New Old
Modular forms 392 256 136
Cusp forms 376 256 120
Eisenstein series 16 0 16

Trace form

\( 256 q - 2048 q^{4} - 64 q^{6} - 26 q^{7} + 66 q^{9} + O(q^{10}) \) \( 256 q - 2048 q^{4} - 64 q^{6} - 26 q^{7} + 66 q^{9} + 234 q^{11} - 230 q^{12} - 10 q^{13} - 1422 q^{14} - 50 q^{15} + 16384 q^{16} - 474 q^{18} + 308 q^{19} + 974 q^{21} + 1998 q^{23} + 1396 q^{24} + 16000 q^{25} + 2304 q^{26} + 870 q^{27} + 832 q^{28} - 2376 q^{29} + 800 q^{30} - 2944 q^{31} + 1172 q^{33} + 984 q^{36} + 1034 q^{37} - 12060 q^{38} + 4706 q^{39} + 4464 q^{41} + 23520 q^{42} - 1408 q^{43} - 23130 q^{44} + 600 q^{45} + 1056 q^{46} + 1220 q^{48} + 3814 q^{49} - 6628 q^{51} + 320 q^{52} - 17928 q^{53} - 4818 q^{54} + 20448 q^{56} + 5990 q^{57} - 11700 q^{60} - 8956 q^{61} + 22364 q^{63} - 131072 q^{64} + 25600 q^{66} + 15260 q^{67} + 40050 q^{68} - 35592 q^{69} - 4800 q^{70} + 25346 q^{72} - 19012 q^{73} + 33300 q^{74} - 9856 q^{76} - 31806 q^{77} + 6544 q^{78} - 10792 q^{79} - 12034 q^{81} + 15840 q^{83} + 10848 q^{84} - 4350 q^{85} + 65574 q^{86} + 9542 q^{87} + 35784 q^{89} + 13950 q^{90} + 18866 q^{91} - 27036 q^{92} - 44994 q^{93} - 2688 q^{94} + 18406 q^{96} - 6346 q^{97} + 27270 q^{98} - 59526 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{5}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(315, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)