↑

Properties

Label 1755.2.l
Level $1755$
Weight $2$
Character orbit 1755.l
Rep. character $\chi_{1755}(991,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $112$
Sturm bound $504$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1755 = 3^{3} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1755.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 528 112 416
Cusp forms 480 112 368
Eisenstein series 48 0 48

Trace form

\( 112 q + 112 q^{4} - 4 q^{7} - 12 q^{8} + O(q^{10}) \) \( 112 q + 112 q^{4} - 4 q^{7} - 12 q^{8} + 8 q^{11} - 2 q^{13} + 112 q^{16} + 16 q^{17} + 2 q^{19} + 24 q^{23} - 56 q^{25} - 4 q^{26} - 16 q^{28} - 4 q^{29} + 8 q^{31} - 24 q^{32} + 16 q^{35} + 2 q^{37} + 4 q^{38} + 4 q^{41} + 8 q^{43} + 64 q^{44} + 36 q^{47} - 60 q^{49} + 10 q^{52} - 64 q^{53} + 40 q^{56} - 72 q^{58} + 64 q^{59} + 14 q^{61} + 50 q^{62} + 148 q^{64} - 2 q^{65} + 14 q^{67} + 74 q^{68} + 24 q^{71} - 28 q^{73} + 32 q^{74} + 8 q^{76} + 56 q^{77} - 4 q^{79} - 16 q^{80} - 18 q^{82} + 6 q^{83} + 12 q^{85} + 138 q^{86} - 8 q^{89} - 16 q^{91} - 28 q^{92} + 36 q^{94} - 72 q^{95} + 2 q^{97} - 48 q^{98} + O(q^{100}) \)

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

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