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Properties

Label 845.2.x
Level $845$
Weight $2$
Character orbit 845.x
Rep. character $\chi_{845}(14,\cdot)$
Character field $\Q(\zeta_{26})$
Dimension $1080$
Newform subspaces $1$
Sturm bound $182$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.x (of order \(26\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 845 \)
Character field: \(\Q(\zeta_{26})\)
Newform subspaces: \( 1 \)
Sturm bound: \(182\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 1128 1128 0
Cusp forms 1080 1080 0
Eisenstein series 48 48 0

Trace form

\( 1080 q + 68 q^{4} - 13 q^{5} - 30 q^{6} + 64 q^{9} + O(q^{10}) \) \( 1080 q + 68 q^{4} - 13 q^{5} - 30 q^{6} + 64 q^{9} - 19 q^{10} - 14 q^{11} - 34 q^{14} + 23 q^{15} - 112 q^{16} - 52 q^{19} + 7 q^{20} - 22 q^{21} - 42 q^{24} - 13 q^{25} - 20 q^{26} - 18 q^{29} + 99 q^{30} - 58 q^{31} - 46 q^{34} - 25 q^{35} - 88 q^{36} - 138 q^{39} - 53 q^{40} - 18 q^{41} - 14 q^{44} - 74 q^{45} - 6 q^{46} + 122 q^{49} - 29 q^{50} + 88 q^{51} + 42 q^{54} - 67 q^{55} - 66 q^{56} + 62 q^{59} - 105 q^{60} - 42 q^{61} + 108 q^{64} - 11 q^{65} - 36 q^{66} + 88 q^{69} - 214 q^{70} - 2 q^{71} - 74 q^{74} + 121 q^{75} - 188 q^{76} - 58 q^{79} - 74 q^{80} - 148 q^{81} - 532 q^{84} - 40 q^{85} + 162 q^{86} - 32 q^{89} - 73 q^{90} - 22 q^{91} + 26 q^{94} - 160 q^{95} + 10 q^{96} - 68 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
845.2.x.a 845.x 845.x $1080$ $6.747$ None \(0\) \(0\) \(-13\) \(0\) $\mathrm{SU}(2)[C_{26}]$