Properties

Label 3600.1.bb
Level 3600
Weight 1
Character orbit bb
Rep. character \(\chi_{3600}(757,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 4
Newforms 2
Sturm bound 720
Trace bound 17

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Defining parameters

Level: \( N \) = \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 3600.bb (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 80 \)
Character field: \(\Q(i)\)
Newforms: \( 2 \)
Sturm bound: \(720\)
Trace bound: \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3600, [\chi])\).

Total New Old
Modular forms 52 8 44
Cusp forms 4 4 0
Eisenstein series 48 4 44

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\(4q \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 4q^{16} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut +\mathstrut 4q^{34} \) \(\mathstrut +\mathstrut 4q^{46} \) \(\mathstrut +\mathstrut 4q^{61} \) \(\mathstrut -\mathstrut 4q^{64} \) \(\mathstrut +\mathstrut 4q^{76} \) \(\mathstrut +\mathstrut 4q^{94} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3600, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3600.1.bb.a \(2\) \(1.797\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}+q^{16}+(-1+i+\cdots)q^{17}+\cdots\)
3600.1.bb.b \(2\) \(1.797\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{8}+q^{16}+(1-i+\cdots)q^{17}+\cdots\)