Properties

Label 300.1.b
Level 300
Weight 1
Character orbit b
Rep. character \(\chi_{300}(149,\cdot)\)
Character field \(\Q\)
Dimension 2
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 15 \)
Character field: \(\Q\)
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 20 2 18
Cusp forms 2 2 0
Eisenstein series 18 0 18

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

\( 2q - 2q^{9} + O(q^{10}) \) \( 2q - 2q^{9} + 2q^{19} - 2q^{21} - 2q^{31} + 2q^{39} - 2q^{61} - 4q^{79} + 2q^{81} + 2q^{91} + O(q^{100}) \)

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.b.a \(2\) \(0.150\) \(\Q(\sqrt{-1}) \) \(D_{3}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-iq^{7}-q^{9}+iq^{13}+q^{19}+\cdots\)