Properties

Label 3600.1.cc
Level 3600
Weight 1
Character orbit cc
Rep. character \(\chi_{3600}(751,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 4
Newforms 2
Sturm bound 720
Trace bound 3

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Defining parameters

Level: \( N \) = \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 3600.cc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 2 \)
Sturm bound: \(720\)
Trace bound: \(3\)

Dimensions

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

Total New Old
Modular forms 88 4 84
Cusp forms 16 4 12
Eisenstein series 72 0 72

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

\(4q \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut -\mathstrut 2q^{41} \) \(\mathstrut +\mathstrut 4q^{49} \) \(\mathstrut -\mathstrut 2q^{61} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut -\mathstrut 2q^{81} \) \(\mathstrut +\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.cc.a \(2\) \(1.797\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-5}) \) None \(0\) \(-1\) \(0\) \(-3\) \(q-\zeta_{6}q^{3}+(-1-\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)
3600.1.cc.b \(2\) \(1.797\) \(\Q(\sqrt{-3}) \) \(D_{6}\) \(\Q(\sqrt{-5}) \) None \(0\) \(1\) \(0\) \(3\) \(q+\zeta_{6}q^{3}+(1+\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}+(\zeta_{6}+\cdots)q^{21}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3600, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 3}\)