↑

Properties

Label 1755.2.j
Level $1755$
Weight $2$
Character orbit 1755.j
Rep. character $\chi_{1755}(406,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $148$
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.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
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 528 148 380
Cusp forms 480 148 332
Eisenstein series 48 0 48

Trace form

\( 148 q - 72 q^{4} + 14 q^{7} + O(q^{10}) \) \( 148 q - 72 q^{4} + 14 q^{7} - 18 q^{13} - 68 q^{16} - 10 q^{19} + 12 q^{22} + 148 q^{25} + 64 q^{28} + 36 q^{31} - 8 q^{34} - 14 q^{37} - 10 q^{43} - 20 q^{46} - 48 q^{49} + 32 q^{52} - 4 q^{61} + 168 q^{64} - 4 q^{67} - 16 q^{73} + 4 q^{76} + 40 q^{79} + 12 q^{82} + 12 q^{88} + 72 q^{91} - 24 q^{94} - 40 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1755, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(351, [\chi])\)\(^{\oplus 2}\)