↑

Properties

Label 1755.2.ba
Level $1755$
Weight $2$
Character orbit 1755.ba
Rep. character $\chi_{1755}(901,\cdot)$
Character field $\Q(\zeta_{6})$
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.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 112 q - 112 q^{4} + O(q^{10}) \) \( 112 q - 112 q^{4} + 2 q^{13} + 112 q^{16} + 16 q^{17} + 6 q^{19} + 24 q^{23} + 56 q^{25} + 12 q^{26} + 20 q^{29} + 24 q^{31} - 16 q^{35} - 6 q^{37} + 44 q^{38} - 12 q^{41} + 8 q^{43} + 36 q^{47} + 52 q^{49} + 10 q^{52} + 32 q^{53} - 40 q^{56} - 14 q^{61} + 26 q^{62} - 76 q^{64} + 2 q^{65} + 42 q^{67} - 74 q^{68} + 24 q^{71} + 8 q^{74} - 24 q^{76} + 56 q^{77} - 8 q^{79} + 18 q^{82} + 18 q^{83} + 6 q^{86} + 36 q^{89} - 12 q^{92} - 36 q^{94} - 56 q^{95} - 6 q^{97} - 48 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1755, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(351, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 2}\)