Properties

Label 945.2.cz
Level 945
Weight 2
Character orbit cz
Rep. character \(\chi_{945}(41,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 576
Newform subspaces 2
Sturm bound 288
Trace bound 3

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Defining parameters

Level: \( N \) = \( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 945.cz (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 189 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(13\)

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

\( 576q - 6q^{9} + O(q^{10}) \) \( 576q - 6q^{9} + 6q^{11} - 24q^{14} - 24q^{21} - 72q^{23} + 36q^{29} + 84q^{36} - 24q^{39} - 60q^{42} + 18q^{49} - 36q^{51} - 126q^{56} - 24q^{57} - 12q^{63} + 288q^{64} - 12q^{65} + 36q^{70} - 72q^{71} - 204q^{72} + 12q^{74} + 54q^{77} - 96q^{78} - 36q^{79} - 6q^{81} + 150q^{84} - 36q^{85} + 12q^{86} - 18q^{91} + 384q^{92} - 48q^{93} + 72q^{98} + 324q^{99} + O(q^{100}) \)

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.cz.a \(288\) \(7.546\) None \(0\) \(-3\) \(0\) \(0\)
945.2.cz.b \(288\) \(7.546\) None \(0\) \(3\) \(0\) \(0\)

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

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