↑

Properties

Label 1575.2.cq
Level $1575$
Weight $2$
Character orbit 1575.cq
Rep. character $\chi_{1575}(121,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $1888$
Sturm bound $480$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1575.cq (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1575 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1575, [\chi])\).

Total New Old
Modular forms 1952 1952 0
Cusp forms 1888 1888 0
Eisenstein series 64 64 0

Trace form

\( 1888 q - 6 q^{2} - 3 q^{3} - 470 q^{4} + 4 q^{5} - 8 q^{6} - 8 q^{7} - 16 q^{8} - 3 q^{9} + O(q^{10}) \) \( 1888 q - 6 q^{2} - 3 q^{3} - 470 q^{4} + 4 q^{5} - 8 q^{6} - 8 q^{7} - 16 q^{8} - 3 q^{9} - 4 q^{10} + 3 q^{11} + 25 q^{12} - 6 q^{13} - 27 q^{14} - 42 q^{15} - 446 q^{16} - 12 q^{17} - 6 q^{19} - 2 q^{20} - 3 q^{21} + 2 q^{22} + 11 q^{23} + 22 q^{24} + 4 q^{25} + 76 q^{26} + 18 q^{27} - 20 q^{28} - 6 q^{29} - 26 q^{30} - 6 q^{31} - 8 q^{32} + 15 q^{33} - 10 q^{34} - 49 q^{35} + 20 q^{36} - 6 q^{37} + 11 q^{38} - 11 q^{39} + 11 q^{40} - 38 q^{41} + 4 q^{42} - 16 q^{43} + 6 q^{44} - 32 q^{45} + 2 q^{46} - 6 q^{47} + 44 q^{48} - 8 q^{49} - 28 q^{50} - 44 q^{51} + 7 q^{52} + 14 q^{53} + q^{54} - 34 q^{55} + 12 q^{56} - 144 q^{57} + 23 q^{58} + 90 q^{59} + 74 q^{60} - 6 q^{61} - 52 q^{62} + 43 q^{63} - 436 q^{64} - 38 q^{65} - 37 q^{66} - 6 q^{67} + 128 q^{68} - 27 q^{69} + 68 q^{70} - 42 q^{71} - 15 q^{72} - 6 q^{73} + 16 q^{74} - 149 q^{75} - 16 q^{76} - 17 q^{77} + 40 q^{78} - 30 q^{79} + 94 q^{80} + 49 q^{81} - 20 q^{82} - 48 q^{83} - 44 q^{84} - 13 q^{85} + 11 q^{86} - 41 q^{87} + 11 q^{88} - 39 q^{89} - 178 q^{90} + 30 q^{91} - 30 q^{92} - 4 q^{93} + 26 q^{94} - 36 q^{95} - 55 q^{96} - 6 q^{97} - 142 q^{98} - 30 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.