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Properties

Label 1764.2.bs
Level $1764$
Weight $2$
Character orbit 1764.bs
Rep. character $\chi_{1764}(71,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $672$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1764.bs (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 588 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 2064 672 1392
Cusp forms 1968 672 1296
Eisenstein series 96 0 96

Trace form

\( 672 q + O(q^{10}) \) \( 672 q + 16 q^{13} - 24 q^{22} + 96 q^{25} + 88 q^{28} - 56 q^{34} + 40 q^{37} + 120 q^{40} + 40 q^{46} - 16 q^{49} - 16 q^{52} - 32 q^{58} + 40 q^{61} + 72 q^{64} + 116 q^{70} + 64 q^{73} + 12 q^{76} + 76 q^{82} - 48 q^{88} - 144 q^{94} - 32 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1764, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 2}\)