Properties

Label 855.2.bc
Level $855$
Weight $2$
Character orbit 855.bc
Rep. character $\chi_{855}(521,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $1$
Sturm bound $240$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(240\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(855, [\chi])\).

Total New Old
Modular forms 256 48 208
Cusp forms 224 48 176
Eisenstein series 32 0 32

Trace form

\( 48 q - 12 q^{4} - 16 q^{7} + O(q^{10}) \) \( 48 q - 12 q^{4} - 16 q^{7} - 12 q^{10} + 48 q^{13} + 4 q^{16} + 8 q^{19} + 24 q^{25} + 24 q^{28} - 36 q^{34} + 24 q^{40} - 16 q^{43} + 48 q^{49} - 24 q^{52} - 64 q^{58} + 64 q^{61} - 112 q^{64} - 48 q^{67} + 72 q^{70} - 16 q^{73} + 80 q^{76} - 80 q^{82} + 16 q^{85} + 48 q^{91} - 48 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(855, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
855.2.bc.a 855.bc 57.f $48$ $6.827$ None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(855, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(855, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)