↑

Properties

Label 1575.4.p
Level $1575$
Weight $4$
Character orbit 1575.p
Rep. character $\chi_{1575}(118,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $356$
Sturm bound $960$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1575.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1575, [\chi])\).

Total New Old
Modular forms 1488 364 1124
Cusp forms 1392 356 1036
Eisenstein series 96 8 88

Trace form

\( 356 q - 4 q^{2} - 14 q^{7} - 56 q^{8} + O(q^{10}) \) \( 356 q - 4 q^{2} - 14 q^{7} - 56 q^{8} + 136 q^{11} - 5288 q^{16} + 228 q^{22} + 92 q^{23} - 48 q^{28} - 912 q^{32} - 548 q^{37} + 100 q^{43} + 4020 q^{46} - 308 q^{53} + 4444 q^{56} - 3092 q^{58} + 636 q^{67} - 744 q^{71} - 1672 q^{77} - 9036 q^{86} + 560 q^{88} - 7180 q^{91} + 4272 q^{92} + 204 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)