Properties

Label 855.2.be
Level $855$
Weight $2$
Character orbit 855.be
Rep. character $\chi_{855}(64,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $6$
Sturm bound $240$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(240\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 256 104 152
Cusp forms 224 96 128
Eisenstein series 32 8 24

Trace form

\( 96 q + 42 q^{4} + 2 q^{5} + O(q^{10}) \) \( 96 q + 42 q^{4} + 2 q^{5} - 2 q^{10} + 16 q^{11} - 14 q^{14} - 34 q^{16} - 14 q^{19} - 4 q^{20} + 4 q^{25} + 4 q^{26} - 14 q^{29} + 6 q^{34} + 14 q^{35} + 10 q^{40} + 4 q^{41} + 68 q^{44} - 24 q^{46} - 88 q^{49} + 56 q^{50} + 16 q^{55} - 116 q^{56} - 38 q^{59} - 24 q^{61} - 40 q^{64} + 20 q^{65} + 6 q^{70} + 48 q^{71} + 42 q^{74} + 22 q^{76} + 10 q^{79} - 20 q^{80} - 38 q^{85} + 56 q^{86} - 30 q^{89} - 40 q^{91} - 84 q^{94} - 28 q^{95} + O(q^{100}) \)

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.be.a 855.be 95.i $4$ $6.827$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+2\zeta_{12}^{2}q^{4}+(-1-\zeta_{12}+\cdots)q^{5}+\cdots\)
855.2.be.b 855.be 95.i $8$ $6.827$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{24}^{5}q^{2}+(-\zeta_{24}^{2}+\zeta_{24}^{4}+\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
855.2.be.c 855.be 95.i $8$ $6.827$ 8.0.12960000.1 \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+(\beta _{4}+\beta _{5}-\beta _{7})q^{2}+(-1+\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots\)
855.2.be.d 855.be 95.i $12$ $6.827$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{5}q^{2}+(-\beta _{2}+\beta _{3}-\beta _{8}-\beta _{9})q^{4}+\cdots\)
855.2.be.e 855.be 95.i $24$ $6.827$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
855.2.be.f 855.be 95.i $40$ $6.827$ None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

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