Properties

Label 1575.2.cj
Level $1575$
Weight $2$
Character orbit 1575.cj
Rep. character $\chi_{1575}(643,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $560$
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.cj (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1008 592 416
Cusp forms 912 560 352
Eisenstein series 96 32 64

Trace form

\( 560 q + 4 q^{2} + 2 q^{7} + 32 q^{8} + O(q^{10}) \) \( 560 q + 4 q^{2} + 2 q^{7} + 32 q^{8} + 248 q^{16} + 8 q^{18} - 24 q^{21} - 12 q^{22} + 12 q^{23} + 32 q^{28} - 48 q^{32} + 16 q^{36} + 16 q^{37} - 38 q^{42} + 4 q^{43} + 64 q^{46} + 8 q^{51} - 64 q^{53} - 4 q^{56} + 112 q^{57} + 44 q^{58} - 24 q^{63} + 4 q^{67} + 32 q^{71} + 20 q^{72} - 26 q^{77} - 76 q^{78} + 80 q^{81} - 184 q^{86} + 60 q^{88} - 16 q^{91} + 68 q^{92} - 88 q^{93} + 120 q^{98} + O(q^{100}) \)

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

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