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Properties

Label 315.10.r
Level $315$
Weight $10$
Character orbit 315.r
Rep. character $\chi_{315}(184,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $856$
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.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 872 872 0
Cusp forms 856 856 0
Eisenstein series 16 16 0

Trace form

\( 856 q - 217092 q^{4} + q^{5} - 3528 q^{6} - 34646 q^{9} + O(q^{10}) \) \( 856 q - 217092 q^{4} + q^{5} - 3528 q^{6} - 34646 q^{9} + 1022 q^{10} + 15414 q^{11} - 59618 q^{14} - 335471 q^{15} + 54527996 q^{16} - 4 q^{19} - 524802 q^{20} - 1950074 q^{21} + 3008964 q^{24} + q^{25} - 10968452 q^{26} + 1558006 q^{29} + 12280145 q^{30} - 4 q^{31} - 1028 q^{34} - 670041 q^{35} + 53925588 q^{36} + 79575508 q^{39} - 2476388 q^{40} - 91540258 q^{41} - 16831492 q^{44} + 26294697 q^{45} + 6431068 q^{46} - 31071548 q^{49} + 78147754 q^{50} - 273367834 q^{51} + 176117160 q^{54} - 42273150 q^{55} + 59224392 q^{56} - 1163266660 q^{59} + 399116529 q^{60} - 24455632 q^{61} - 13422819344 q^{64} - 478917614 q^{65} - 1072733336 q^{66} + 558253990 q^{69} - 40036389 q^{70} - 218822280 q^{71} + 236208902 q^{74} - 1503638553 q^{75} + 526332 q^{76} + 288112892 q^{79} + 221960273 q^{80} - 592013950 q^{81} + 918088514 q^{84} - 1953127 q^{85} - 1716965164 q^{86} + 3494945758 q^{89} + 5089914185 q^{90} - 161414436 q^{91} - 1515382148 q^{94} - 331962406 q^{95} - 6618701652 q^{96} - 1989028650 q^{99} + O(q^{100}) \)

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.