↑

Properties

Label 315.5.ca
Level $315$
Weight $5$
Character orbit 315.ca
Rep. character $\chi_{315}(37,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $312$
Sturm bound $240$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 315.ca (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(240\)

Dimensions

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

Total New Old
Modular forms 800 328 472
Cusp forms 736 312 424
Eisenstein series 64 16 48

Trace form

\( 312 q + 2 q^{2} + 20 q^{5} - 114 q^{7} + 252 q^{8} + O(q^{10}) \) \( 312 q + 2 q^{2} + 20 q^{5} - 114 q^{7} + 252 q^{8} + 62 q^{10} - 8 q^{11} - 8 q^{13} + 8660 q^{16} - 868 q^{17} + 1032 q^{20} + 56 q^{22} + 662 q^{23} - 532 q^{25} + 52 q^{26} + 2562 q^{28} + 816 q^{31} + 1286 q^{32} + 244 q^{35} + 1808 q^{37} + 4956 q^{38} + 562 q^{40} - 5984 q^{41} + 5492 q^{43} + 5588 q^{46} + 4712 q^{47} + 15572 q^{50} - 9696 q^{52} - 8668 q^{53} - 13640 q^{55} - 13044 q^{56} + 7270 q^{58} - 2284 q^{61} - 26336 q^{62} + 7628 q^{65} + 2598 q^{67} + 25864 q^{68} + 13768 q^{70} + 22360 q^{71} - 25672 q^{73} - 54640 q^{76} + 16592 q^{77} - 18904 q^{80} - 1874 q^{82} - 15052 q^{83} - 18912 q^{85} - 1400 q^{86} - 3456 q^{88} + 33768 q^{91} - 32932 q^{92} + 17088 q^{95} + 41832 q^{97} + 92286 q^{98} + O(q^{100}) \)

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

\( S_{5}^{\mathrm{old}}(315, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)