Properties

Label 148.1.f
Level 148
Weight 1
Character orbit f
Rep. character \(\chi_{148}(105,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 2
Newforms 1
Sturm bound 19
Trace bound 0

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Defining parameters

Level: \( N \) = \( 148 = 2^{2} \cdot 37 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 148.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 37 \)
Character field: \(\Q(i)\)
Newforms: \( 1 \)
Sturm bound: \(19\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(148, [\chi])\).

Total New Old
Modular forms 8 2 6
Cusp forms 2 2 0
Eisenstein series 6 0 6

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 0 0 2 0

Trace form

\(2q \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 2q^{23} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut +\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 2q^{51} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut +\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut 2q^{71} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut -\mathstrut 2q^{79} \) \(\mathstrut -\mathstrut 2q^{81} \) \(\mathstrut -\mathstrut 2q^{83} \) \(\mathstrut -\mathstrut 2q^{87} \) \(\mathstrut -\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(148, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
148.1.f.a \(2\) \(0.074\) \(\Q(\sqrt{-1}) \) \(S_{4}\) None None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{3}-q^{7}-iq^{11}+(-1-i)q^{17}+\cdots\)