Properties

Label 855.2.c
Level $855$
Weight $2$
Character orbit 855.c
Rep. character $\chi_{855}(514,\cdot)$
Character field $\Q$
Dimension $44$
Newform subspaces $7$
Sturm bound $240$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(240\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(11\)

Dimensions

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

Total New Old
Modular forms 128 44 84
Cusp forms 112 44 68
Eisenstein series 16 0 16

Trace form

\( 44 q - 42 q^{4} + q^{5} + O(q^{10}) \) \( 44 q - 42 q^{4} + q^{5} - 12 q^{10} + 2 q^{11} - 4 q^{14} + 62 q^{16} + 4 q^{19} - 8 q^{20} + 25 q^{25} + 20 q^{26} + 8 q^{29} - 8 q^{31} - 40 q^{34} + q^{35} + 16 q^{40} - 16 q^{41} - 20 q^{44} + 68 q^{46} - 66 q^{49} + 16 q^{50} + 11 q^{55} - 28 q^{56} - 28 q^{59} - 2 q^{61} - 102 q^{64} + 16 q^{65} - 24 q^{70} - 12 q^{71} + 36 q^{74} - 10 q^{76} + 26 q^{80} + 9 q^{85} + 52 q^{86} + 36 q^{89} + 64 q^{91} + 20 q^{94} + q^{95} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
855.2.c.a $2$ $6.827$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{2}+q^{4}+(-2-i)q^{5}+2iq^{7}+\cdots\)
855.2.c.b $2$ $6.827$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{2}+q^{4}+(1+2i)q^{5}+2iq^{7}+\cdots\)
855.2.c.c $2$ $6.827$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+iq^{2}+q^{4}+(2-i)q^{5}-2iq^{7}+3iq^{8}+\cdots\)
855.2.c.d $6$ $6.827$ 6.0.16516096.1 None \(0\) \(0\) \(1\) \(0\) \(q-\beta _{5}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{3}+\beta _{5})q^{5}+\cdots\)
855.2.c.e $6$ $6.827$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+(-\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots\)
855.2.c.f $12$ $6.827$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{9}q^{2}+(-1+\beta _{2})q^{4}-\beta _{8}q^{5}-\beta _{6}q^{7}+\cdots\)
855.2.c.g $14$ $6.827$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(855, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)