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Properties

Label 855.2.cg
Level $855$
Weight $2$
Character orbit 855.cg
Rep. character $\chi_{855}(77,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $432$
Newform subspaces $4$
Sturm bound $240$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.cg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 4 \)
Sturm bound: \(240\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 496 432 64
Cusp forms 464 432 32
Eisenstein series 32 0 32

Trace form

\( 432 q + 4 q^{3} - 16 q^{6} + O(q^{10}) \) \( 432 q + 4 q^{3} - 16 q^{6} - 24 q^{11} - 16 q^{12} + 16 q^{15} + 216 q^{16} - 48 q^{20} + 8 q^{21} - 12 q^{25} - 56 q^{27} - 88 q^{30} - 120 q^{32} + 28 q^{33} + 64 q^{36} - 24 q^{37} - 24 q^{41} - 56 q^{42} - 48 q^{46} - 48 q^{47} + 132 q^{48} - 24 q^{51} - 24 q^{55} - 96 q^{56} + 24 q^{58} - 156 q^{60} - 24 q^{61} - 76 q^{63} - 88 q^{66} - 12 q^{67} + 20 q^{72} + 32 q^{75} + 140 q^{78} - 96 q^{82} + 120 q^{83} - 48 q^{85} - 48 q^{88} + 188 q^{90} + 48 q^{91} + 228 q^{92} - 112 q^{93} - 48 q^{96} - 60 q^{97} + O(q^{100}) \)

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.cg.a 855.cg 45.l $4$ $6.827$ \(\Q(\zeta_{12})\) None \(-4\) \(-6\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1+\zeta_{12}-\zeta_{12}^{3})q^{2}+(-2+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
855.2.cg.b 855.cg 45.l $4$ $6.827$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(4\) \(-6\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
855.2.cg.c 855.cg 45.l $208$ $6.827$ None \(6\) \(8\) \(0\) \(6\) $\mathrm{SU}(2)[C_{12}]$
855.2.cg.d 855.cg 45.l $216$ $6.827$ None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

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

\( S_{2}^{\mathrm{old}}(855, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)