Properties

Label 945.2.bs
Level 945
Weight 2
Character orbit bs
Rep. character \(\chi_{945}(16,\cdot)\)
Character field \(\Q(\zeta_{9})\)
Dimension 576
Newform subspaces 2
Sturm bound 288
Trace bound 1

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Defining parameters

Level: \( N \) \(=\) \( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 945.bs (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 189 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 888 576 312
Cusp forms 840 576 264
Eisenstein series 48 0 48

Trace form

\( 576q + 6q^{6} + 12q^{9} + O(q^{10}) \) \( 576q + 6q^{6} + 12q^{9} + 12q^{11} + 54q^{14} - 48q^{17} - 24q^{21} + 18q^{23} + 120q^{24} + 18q^{29} - 36q^{33} + 78q^{36} - 120q^{38} - 24q^{39} - 12q^{41} - 30q^{42} + 18q^{45} + 36q^{47} - 132q^{48} + 36q^{49} - 36q^{51} - 30q^{54} - 120q^{56} - 24q^{57} - 60q^{59} + 18q^{61} - 162q^{62} - 96q^{63} - 288q^{64} - 6q^{65} + 30q^{68} - 18q^{70} + 24q^{71} - 204q^{72} + 72q^{73} - 156q^{74} - 90q^{77} + 96q^{78} - 18q^{79} - 84q^{80} + 12q^{81} + 60q^{83} - 108q^{84} + 36q^{85} + 6q^{86} - 60q^{87} + 36q^{91} - 48q^{92} - 24q^{93} - 36q^{94} + 216q^{96} - 48q^{98} - 108q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
945.2.bs.a \(276\) \(7.546\) None \(0\) \(-6\) \(0\) \(0\)
945.2.bs.b \(300\) \(7.546\) None \(0\) \(6\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(945, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(945, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database