↑

Properties

Label 1512.2.en
Level $1512$
Weight $2$
Character orbit 1512.en
Rep. character $\chi_{1512}(139,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $1704$
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.en (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1512 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 1752 1752 0
Cusp forms 1704 1704 0
Eisenstein series 48 48 0

Trace form

\( 1704 q - 12 q^{2} - 12 q^{4} - 6 q^{8} - 24 q^{9} + O(q^{10}) \) \( 1704 q - 12 q^{2} - 12 q^{4} - 6 q^{8} - 24 q^{9} - 24 q^{11} + 9 q^{14} - 12 q^{16} - 12 q^{18} - 12 q^{22} - 24 q^{25} - 12 q^{28} - 30 q^{30} - 42 q^{32} - 6 q^{35} + 48 q^{36} - 36 q^{42} - 24 q^{43} - 6 q^{44} - 6 q^{46} - 12 q^{49} + 18 q^{50} - 60 q^{51} + 57 q^{56} - 60 q^{57} - 12 q^{58} - 42 q^{60} - 6 q^{64} - 24 q^{65} - 24 q^{67} + 21 q^{70} + 78 q^{72} - 66 q^{74} + 24 q^{78} - 24 q^{81} - 78 q^{84} - 90 q^{86} + 36 q^{88} - 6 q^{91} + 108 q^{92} - 60 q^{98} - 24 q^{99} + O(q^{100}) \)

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.