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Properties

Label 1755.2.ci
Level $1755$
Weight $2$
Character orbit 1755.ci
Rep. character $\chi_{1755}(163,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $448$
Sturm bound $504$

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Defining parameters

Level: \( N \) \(=\) \( 1755 = 3^{3} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1755.ci (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1755, [\chi])\).

Total New Old
Modular forms 1056 448 608
Cusp forms 960 448 512
Eisenstein series 96 0 96

Trace form

\( 448 q - 224 q^{4} + O(q^{10}) \) \( 448 q - 224 q^{4} + 24 q^{13} - 224 q^{16} + 16 q^{19} + 8 q^{22} + 32 q^{25} + 8 q^{31} - 16 q^{34} - 144 q^{37} - 24 q^{40} - 20 q^{43} + 16 q^{46} + 232 q^{49} - 92 q^{52} + 16 q^{55} - 120 q^{58} - 8 q^{61} + 448 q^{64} - 48 q^{67} + 68 q^{70} + 32 q^{73} - 32 q^{76} + 56 q^{82} + 100 q^{85} + 152 q^{88} - 8 q^{91} + 24 q^{94} + 44 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1755, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1755, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1755, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 2}\)