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Properties

Label 1755.2.cd
Level $1755$
Weight $2$
Character orbit 1755.cd
Rep. character $\chi_{1755}(253,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $320$
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.cd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 585 \)
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 352 704
Cusp forms 960 320 640
Eisenstein series 96 32 64

Trace form

\( 320 q - 304 q^{4} + 2 q^{5} + 2 q^{7} + O(q^{10}) \) \( 320 q - 304 q^{4} + 2 q^{5} + 2 q^{7} - 16 q^{10} + 12 q^{11} - 2 q^{13} - 48 q^{14} + 264 q^{16} + 12 q^{17} + 30 q^{20} - 4 q^{22} - 2 q^{23} - 24 q^{28} - 4 q^{31} + 8 q^{34} + 46 q^{35} - 4 q^{37} + 40 q^{38} + 28 q^{40} - 4 q^{41} - 6 q^{43} - 8 q^{44} - 16 q^{46} + 14 q^{47} - 112 q^{49} - 56 q^{50} - 30 q^{52} + 16 q^{53} - 4 q^{55} + 108 q^{56} + 28 q^{58} + 16 q^{59} + 4 q^{61} + 28 q^{62} - 192 q^{64} - 58 q^{65} - 6 q^{67} - 62 q^{68} + 10 q^{70} - 20 q^{76} + 44 q^{77} - 4 q^{80} + 20 q^{82} - 8 q^{83} - 16 q^{85} - 68 q^{86} - 8 q^{88} - 16 q^{91} + 32 q^{92} + 48 q^{94} - 6 q^{97} + 282 q^{98} + O(q^{100}) \)

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

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