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Properties

Label 945.2.cu
Level $945$
Weight $2$
Character orbit 945.cu
Rep. character $\chi_{945}(184,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $840$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 945.cu (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 945 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(945, [\chi])\).

Total New Old
Modular forms 888 888 0
Cusp forms 840 840 0
Eisenstein series 48 48 0

Trace form

\( 840 q - 6 q^{4} - 3 q^{5} - 30 q^{6} - 12 q^{9} + O(q^{10}) \) \( 840 q - 6 q^{4} - 3 q^{5} - 30 q^{6} - 12 q^{9} - 6 q^{10} - 18 q^{14} - 24 q^{15} + 6 q^{16} - 12 q^{19} - 6 q^{20} - 30 q^{21} - 42 q^{24} - 3 q^{25} - 84 q^{26} - 6 q^{29} + 15 q^{30} - 6 q^{31} - 12 q^{34} - 12 q^{35} - 42 q^{36} + 12 q^{39} - 36 q^{40} - 12 q^{41} + 6 q^{44} - 3 q^{45} + 6 q^{46} - 30 q^{49} - 48 q^{50} + 66 q^{51} + 36 q^{54} - 24 q^{55} - 60 q^{56} - 6 q^{59} - 63 q^{60} + 30 q^{61} + 324 q^{64} - 9 q^{65} - 6 q^{66} - 36 q^{69} + 48 q^{70} - 12 q^{71} - 30 q^{74} + 48 q^{75} - 48 q^{76} - 24 q^{79} - 30 q^{80} - 72 q^{81} - 300 q^{84} + 3 q^{85} + 42 q^{86} - 300 q^{89} - 39 q^{90} - 6 q^{91} - 42 q^{94} + 21 q^{95} + 150 q^{96} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(945, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
945.2.cu.a 945.cu 945.bu $840$ $7.546$ None \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{18}]$