Properties

Label 1156.1.f
Level $1156$
Weight $1$
Character orbit 1156.f
Rep. character $\chi_{1156}(251,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $2$
Sturm bound $153$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1156 = 2^{2} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1156.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 68 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(153\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1156, [\chi])\).

Total New Old
Modular forms 44 32 12
Cusp forms 8 4 4
Eisenstein series 36 28 8

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

\( 4q - 4q^{4} + 2q^{5} + O(q^{10}) \) \( 4q - 4q^{4} + 2q^{5} - 2q^{10} + 4q^{13} + 4q^{16} - 2q^{20} - 2q^{29} + 2q^{37} + 2q^{40} - 2q^{41} - 2q^{45} - 4q^{50} - 4q^{52} + 2q^{58} + 2q^{61} - 4q^{64} - 2q^{73} - 2q^{74} + 2q^{80} - 4q^{81} - 2q^{82} + 4q^{89} - 2q^{90} + 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1156, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1156.1.f.a \(2\) \(0.577\) \(\Q(\sqrt{-1}) \) \(D_{2}\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \) \(\Q(\sqrt{17}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{8}-iq^{9}+q^{13}+\cdots\)
1156.1.f.b \(2\) \(0.577\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q-iq^{2}-q^{4}+(1-i)q^{5}+iq^{8}-iq^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1156, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1156, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 2}\)