Properties

Label 3600.1.bh
Level 3600
Weight 1
Character orbit bh
Rep. character \(\chi_{3600}(2593,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 6
Newforms 2
Sturm bound 720
Trace bound 1

Related objects

Downloads

Learn more about

Defining parameters

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

Dimensions

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

Total New Old
Modular forms 172 8 164
Cusp forms 28 6 22
Eisenstein series 144 2 142

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\(6q \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut +\mathstrut 12q^{91} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.bh.a \(2\) \(1.797\) \(\Q(\sqrt{-1}) \) \(D_{2}\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{19}+q^{31}-iq^{49}+q^{61}+iq^{79}+\cdots\)
3600.1.bh.b \(4\) \(1.797\) \(\Q(i, \sqrt{6})\) \(D_{6}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{7}+\beta _{3}q^{13}+\beta _{2}q^{19}-q^{31}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 3}\)