↑

Properties

Label 1575.2.bm
Level $1575$
Weight $2$
Character orbit 1575.bm
Rep. character $\chi_{1575}(776,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $292$
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.bm (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 \(M_{2}(1575, [\chi])\).

Total New Old
Modular forms 504 316 188
Cusp forms 456 292 164
Eisenstein series 48 24 24

Trace form

\( 292 q + 6 q^{2} + 142 q^{4} + 12 q^{9} + O(q^{10}) \) \( 292 q + 6 q^{2} + 142 q^{4} + 12 q^{9} - 24 q^{11} - 18 q^{14} - 138 q^{16} + 2 q^{18} + 6 q^{21} + 10 q^{22} + 12 q^{23} - 8 q^{28} - 30 q^{29} + 12 q^{32} + 78 q^{36} + 12 q^{37} + 30 q^{42} - 6 q^{43} + 8 q^{46} - 4 q^{49} - 30 q^{51} - 114 q^{56} - 18 q^{57} - 2 q^{58} + 28 q^{63} - 240 q^{64} + 16 q^{67} - 116 q^{72} - 24 q^{74} + 78 q^{77} + 144 q^{78} + 10 q^{79} - 48 q^{81} + 54 q^{84} - 72 q^{86} - 34 q^{88} - 4 q^{91} - 6 q^{92} - 42 q^{93} - 84 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)