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
Newforms 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: \(\Q(\zeta_{9})\)
Newforms: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(945, [\chi])\) into irreducible Hecke orbits

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

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