↑

Properties

Label 315.10.bl
Level $315$
Weight $10$
Character orbit 315.bl
Rep. character $\chi_{315}(41,\cdot)$
Character field $\Q(\zeta_{6})$
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.bl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
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 872 576 296
Cusp forms 856 576 280
Eisenstein series 16 0 16

Trace form

\( 576 q + 73728 q^{4} - 684 q^{7} + 35492 q^{9} + O(q^{10}) \) \( 576 q + 73728 q^{4} - 684 q^{7} + 35492 q^{9} + 46236 q^{11} - 867414 q^{14} - 132500 q^{15} - 18874368 q^{16} + 3060652 q^{18} - 4003248 q^{21} + 10197432 q^{23} - 112500000 q^{25} - 1400832 q^{28} - 17450244 q^{29} + 4760000 q^{30} - 45800592 q^{36} + 25907616 q^{37} - 54569028 q^{39} + 155341806 q^{42} + 64140048 q^{43} + 25716096 q^{46} + 39676266 q^{49} - 275396820 q^{51} - 292708890 q^{56} - 2977824 q^{57} - 241252500 q^{60} - 360072568 q^{63} - 9663676416 q^{64} + 69240000 q^{65} + 556997112 q^{67} + 156060000 q^{70} + 1211599340 q^{72} + 2390104500 q^{74} + 1498681872 q^{77} + 37999380 q^{78} - 446946804 q^{79} - 1242450556 q^{81} - 1852748898 q^{84} + 255015000 q^{85} + 2082564348 q^{86} + 3509400600 q^{91} + 7354500888 q^{92} - 5138164752 q^{93} - 11649011096 q^{99} + O(q^{100}) \)

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

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