Properties

Label 845.2.l
Level $845$
Weight $2$
Character orbit 845.l
Rep. character $\chi_{845}(654,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $136$
Newform subspaces $7$
Sturm bound $182$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 7 \)
Sturm bound: \(182\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(845, [\chi])\).

Total New Old
Modular forms 208 176 32
Cusp forms 152 136 16
Eisenstein series 56 40 16

Trace form

\( 136 q - 58 q^{4} + 6 q^{6} + 56 q^{9} + O(q^{10}) \) \( 136 q - 58 q^{4} + 6 q^{6} + 56 q^{9} + 8 q^{10} - 60 q^{14} + 6 q^{15} - 26 q^{16} + 12 q^{19} - 24 q^{20} - 12 q^{24} + 4 q^{25} - 4 q^{29} + 44 q^{30} - 10 q^{35} + 16 q^{36} - 20 q^{40} - 12 q^{45} - 42 q^{46} - 20 q^{49} + 12 q^{50} + 16 q^{51} - 30 q^{54} + 22 q^{55} + 60 q^{56} + 60 q^{59} - 28 q^{61} + 8 q^{64} - 20 q^{66} - 12 q^{69} - 12 q^{71} + 50 q^{74} + 14 q^{75} - 6 q^{76} - 96 q^{79} - 18 q^{80} + 36 q^{81} + 6 q^{84} - 42 q^{85} - 48 q^{89} - 116 q^{90} - 72 q^{94} + 20 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(845, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
845.2.l.a $4$ $6.747$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(4\) \(0\) \(q+(-1+\zeta_{12}^{2})q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
845.2.l.b $4$ $6.747$ \(\Q(\zeta_{12})\) None \(2\) \(0\) \(-4\) \(0\) \(q+(1-\zeta_{12}^{2})q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
845.2.l.c $8$ $6.747$ 8.0.49787136.1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{5})q^{2}+(-\beta _{3}-\beta _{5})q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots\)
845.2.l.d $12$ $6.747$ 12.0.\(\cdots\).1 None \(-6\) \(0\) \(4\) \(4\) \(q+(-1+\beta _{1}-\beta _{7}+\beta _{10})q^{2}-\beta _{5}q^{3}+\cdots\)
845.2.l.e $12$ $6.747$ 12.0.\(\cdots\).1 None \(6\) \(0\) \(-4\) \(-4\) \(q+(1-\beta _{1}+\beta _{7}-\beta _{10})q^{2}+\beta _{5}q^{3}+\cdots\)
845.2.l.f $24$ $6.747$ None \(0\) \(0\) \(0\) \(0\)
845.2.l.g $72$ $6.747$ None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(845, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(845, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)