Properties

Label 300.1.l
Level 300
Weight 1
Character orbit l
Rep. character \(\chi_{300}(107,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 4
Newforms 1
Sturm bound 60
Trace bound 0

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Defining parameters

Level: \( N \) = \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 300.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 60 \)
Character field: \(\Q(i)\)
Newforms: \( 1 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(300, [\chi])\).

Total New Old
Modular forms 28 12 16
Cusp forms 4 4 0
Eisenstein series 24 8 16

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

\( 4q - 4q^{6} + O(q^{10}) \) \( 4q - 4q^{6} - 4q^{16} + 4q^{36} + 8q^{46} - 8q^{61} - 4q^{81} + 4q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(300, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
300.1.l.a \(4\) \(0.150\) \(\Q(\zeta_{8})\) \(D_{2}\) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-q^{6}+\cdots\)