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Properties

Label 855.2.dl
Level $855$
Weight $2$
Character orbit 855.dl
Rep. character $\chi_{855}(127,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $576$
Newform subspaces $3$
Sturm bound $240$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.dl (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{36})\)
Newform subspaces: \( 3 \)
Sturm bound: \(240\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 1536 624 912
Cusp forms 1344 576 768
Eisenstein series 192 48 144

Trace form

\( 576 q + 12 q^{2} + 12 q^{5} + 18 q^{8} + O(q^{10}) \) \( 576 q + 12 q^{2} + 12 q^{5} + 18 q^{8} - 12 q^{10} + 12 q^{11} - 12 q^{13} - 60 q^{16} + 30 q^{17} - 36 q^{20} + 24 q^{22} - 24 q^{23} - 36 q^{25} + 72 q^{26} - 36 q^{31} - 6 q^{32} + 30 q^{35} + 78 q^{38} + 54 q^{40} + 60 q^{41} + 24 q^{43} - 36 q^{46} - 126 q^{50} - 6 q^{53} + 18 q^{55} - 168 q^{58} + 108 q^{62} - 72 q^{65} - 84 q^{67} + 30 q^{68} - 60 q^{70} + 24 q^{71} + 6 q^{73} - 180 q^{76} + 48 q^{77} + 36 q^{80} - 84 q^{82} + 12 q^{83} - 84 q^{85} + 84 q^{86} - 198 q^{88} - 24 q^{91} + 120 q^{92} - 24 q^{97} - 102 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.dl.a 855.dl 95.r $96$ $6.827$ None \(12\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{36}]$
855.2.dl.b 855.dl 95.r $240$ $6.827$ None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{36}]$
855.2.dl.c 855.dl 95.r $240$ $6.827$ None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{36}]$

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

\( S_{2}^{\mathrm{old}}(855, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)