↑

Properties

Label 1764.2.be
Level $1764$
Weight $2$
Character orbit 1764.be
Rep. character $\chi_{1764}(863,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
Sturm bound $672$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1764.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 84 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1764, [\chi])\).

Total New Old
Modular forms 736 160 576
Cusp forms 608 160 448
Eisenstein series 128 0 128

Trace form

\( 160 q + O(q^{10}) \) \( 160 q - 16 q^{13} - 8 q^{16} + 40 q^{22} + 72 q^{25} + 16 q^{34} - 8 q^{37} + 52 q^{40} + 28 q^{46} + 52 q^{52} + 40 q^{58} + 16 q^{61} - 168 q^{64} + 8 q^{73} - 72 q^{76} - 68 q^{82} + 64 q^{85} - 64 q^{88} - 60 q^{94} + 176 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1764, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1764, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1764, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)