Properties

Label 360.1.p
Level 360
Weight 1
Character orbit p
Rep. character \(\chi_{360}(19,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 2
Sturm bound 72
Trace bound 2

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Defining parameters

Level: \( N \) = \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 360.p (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 40 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(360, [\chi])\).

Total New Old
Modular forms 10 4 6
Cusp forms 2 2 0
Eisenstein series 8 2 6

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2q + 2q^{4} + O(q^{10}) \) \( 2q + 2q^{4} - 2q^{10} + 2q^{16} - 4q^{19} + 2q^{25} - 2q^{40} - 4q^{46} - 2q^{49} + 2q^{64} - 4q^{76} + 4q^{94} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(360, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
360.1.p.a \(1\) \(0.180\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{6}) \) \(-1\) \(0\) \(1\) \(0\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+q^{16}+\cdots\)
360.1.p.b \(1\) \(0.180\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{6}) \) \(1\) \(0\) \(-1\) \(0\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{16}+\cdots\)