Properties

Label 945.2.cs
Level 945
Weight 2
Character orbit cs
Rep. character \(\chi_{945}(104,\cdot)\)
Character field \(\Q(\zeta_{18})\)
Dimension 840
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.cs (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 945 \)
Character field: \(\Q(\zeta_{18})\)
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 888 888 0
Cusp forms 840 840 0
Eisenstein series 48 48 0

Trace form

\(840q \) \(\mathstrut -\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut 30q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(840q \) \(\mathstrut -\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut 30q^{9} \) \(\mathstrut -\mathstrut 30q^{11} \) \(\mathstrut -\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 12q^{25} \) \(\mathstrut +\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 78q^{30} \) \(\mathstrut -\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 12q^{36} \) \(\mathstrut -\mathstrut 108q^{39} \) \(\mathstrut -\mathstrut 36q^{44} \) \(\mathstrut -\mathstrut 12q^{46} \) \(\mathstrut +\mathstrut 6q^{49} \) \(\mathstrut +\mathstrut 24q^{50} \) \(\mathstrut -\mathstrut 60q^{51} \) \(\mathstrut +\mathstrut 120q^{56} \) \(\mathstrut -\mathstrut 150q^{60} \) \(\mathstrut -\mathstrut 348q^{64} \) \(\mathstrut -\mathstrut 18q^{65} \) \(\mathstrut +\mathstrut 21q^{70} \) \(\mathstrut -\mathstrut 36q^{71} \) \(\mathstrut -\mathstrut 48q^{74} \) \(\mathstrut -\mathstrut 60q^{79} \) \(\mathstrut +\mathstrut 54q^{81} \) \(\mathstrut +\mathstrut 150q^{84} \) \(\mathstrut -\mathstrut 42q^{85} \) \(\mathstrut -\mathstrut 192q^{86} \) \(\mathstrut -\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 210q^{95} \) \(\mathstrut +\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.cs.a \(24\) \(7.546\) \(\Q(\sqrt{-35}) \) \(0\) \(0\) \(0\) \(0\)
945.2.cs.b \(816\) \(7.546\) None \(0\) \(0\) \(0\) \(0\)