↑

Properties

Label 1512.2.cc
Level $1512$
Weight $2$
Character orbit 1512.cc
Rep. character $\chi_{1512}(125,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $184$
Sturm bound $576$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1512.cc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 504 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1512, [\chi])\).

Total New Old
Modular forms 600 200 400
Cusp forms 552 184 368
Eisenstein series 48 16 32

Trace form

\( 184 q + 6 q^{2} - 2 q^{4} - 2 q^{7} + O(q^{10}) \) \( 184 q + 6 q^{2} - 2 q^{4} - 2 q^{7} - 12 q^{14} - 2 q^{16} + 6 q^{22} + 12 q^{23} + 72 q^{25} + 4 q^{28} - 24 q^{32} - 16 q^{46} - 2 q^{49} + 36 q^{50} + 24 q^{56} + 6 q^{58} - 8 q^{64} + 12 q^{65} - 6 q^{70} - 48 q^{74} - 4 q^{79} + 144 q^{86} - 18 q^{88} - 54 q^{92} + 72 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1512, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1512, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1512, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)