↑

Properties

Label 315.10.k
Level $315$
Weight $10$
Character orbit 315.k
Rep. character $\chi_{315}(16,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $576$
Sturm bound $480$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 315.k (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 872 576 296
Cusp forms 856 576 280
Eisenstein series 16 0 16

Trace form

\( 576 q - 73728 q^{4} + 5000 q^{5} + 4544 q^{6} + 684 q^{7} + 16050 q^{9} + O(q^{10}) \) \( 576 q - 73728 q^{4} + 5000 q^{5} + 4544 q^{6} + 684 q^{7} + 16050 q^{9} + 30824 q^{11} - 110660 q^{12} + 64872 q^{13} + 641988 q^{14} - 132500 q^{15} - 18874368 q^{16} - 1336336 q^{17} - 2593836 q^{18} + 446760 q^{19} - 1920000 q^{20} + 232970 q^{21} - 3399144 q^{23} - 7793396 q^{24} + 225000000 q^{25} - 3674240 q^{26} - 704604 q^{27} + 700416 q^{28} + 1558010 q^{29} + 4760000 q^{30} - 7808760 q^{31} - 14252140 q^{32} - 6089272 q^{33} - 76113480 q^{36} - 6476904 q^{37} + 48637048 q^{38} - 6628696 q^{39} + 36618142 q^{41} - 6640332 q^{42} + 32070024 q^{43} + 23470402 q^{44} + 10353750 q^{45} - 6429024 q^{46} - 156501076 q^{47} + 261417836 q^{48} + 70747812 q^{49} + 106104524 q^{51} - 132857856 q^{52} + 65919960 q^{53} - 264363600 q^{54} + 757989678 q^{56} - 90501904 q^{57} + 24318500 q^{59} + 82893750 q^{60} + 150612066 q^{61} - 148967880 q^{62} - 522436168 q^{63} + 9663676416 q^{64} - 23080000 q^{65} - 1305374096 q^{66} - 278498556 q^{67} + 1376862116 q^{68} - 975974784 q^{69} + 156060000 q^{70} - 907948464 q^{71} - 2013802504 q^{72} + 690199776 q^{73} + 329924336 q^{74} + 457482240 q^{76} - 1405254992 q^{77} + 1666830376 q^{78} + 325811664 q^{79} - 1146880000 q^{80} - 1405909882 q^{81} - 3517291268 q^{83} + 971389344 q^{84} - 255015000 q^{85} + 561266732 q^{86} - 1180021612 q^{87} + 902292034 q^{89} - 902801250 q^{90} + 39409380 q^{91} + 3672596900 q^{92} - 1735640832 q^{93} + 757695168 q^{94} + 7898520610 q^{96} + 452087856 q^{97} + 3950188298 q^{98} + 3387188460 q^{99} + O(q^{100}) \)

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.

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

\( S_{10}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)