↑

Properties

Label 1575.2.de
Level $1575$
Weight $2$
Character orbit 1575.de
Rep. character $\chi_{1575}(41,\cdot)$
Character field $\Q(\zeta_{30})$
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.de (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1575 \)
Character field: \(\Q(\zeta_{30})\)
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

\( 1888 q - 18 q^{2} - 238 q^{4} - 8 q^{7} - 12 q^{9} + O(q^{10}) \) \( 1888 q - 18 q^{2} - 238 q^{4} - 8 q^{7} - 12 q^{9} - 18 q^{11} - 9 q^{14} + 16 q^{15} + 210 q^{16} - 32 q^{18} - 3 q^{21} + 10 q^{22} - 42 q^{23} - 8 q^{25} + 20 q^{28} - 18 q^{29} - 64 q^{30} - 36 q^{32} - 10 q^{36} - 24 q^{37} - 52 q^{39} - 46 q^{42} - 16 q^{43} - 8 q^{46} - 8 q^{49} + 36 q^{50} - 32 q^{51} + 66 q^{56} + 120 q^{57} - 14 q^{58} + 56 q^{60} + 4 q^{63} + 336 q^{64} + 54 q^{65} - 6 q^{67} + 36 q^{70} - 72 q^{72} - 24 q^{74} - 33 q^{77} + 76 q^{78} + 18 q^{79} + 92 q^{81} - 15 q^{84} + 2 q^{85} + 42 q^{86} - 78 q^{88} - 54 q^{91} + 114 q^{92} - 160 q^{93} - 102 q^{95} - 12 q^{99} + O(q^{100}) \)

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.