Properties

Label 3332.1.m
Level $3332$
Weight $1$
Character orbit 3332.m
Rep. character $\chi_{3332}(2843,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $6$
Newform subspaces $3$
Sturm bound $504$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3332.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 68 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(504\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3332, [\chi])\).

Total New Old
Modular forms 44 26 18
Cusp forms 12 6 6
Eisenstein series 32 20 12

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

\( 6 q - 6 q^{4} + 2 q^{5} + O(q^{10}) \) \( 6 q - 6 q^{4} + 2 q^{5} - 2 q^{10} + 6 q^{16} + 2 q^{17} + 2 q^{18} - 2 q^{20} - 2 q^{29} + 2 q^{37} + 2 q^{40} - 2 q^{41} - 2 q^{45} + 2 q^{50} - 6 q^{58} + 2 q^{61} - 6 q^{64} - 8 q^{65} - 2 q^{68} - 2 q^{72} - 2 q^{73} + 6 q^{74} + 2 q^{80} - 6 q^{81} - 2 q^{82} - 2 q^{85} - 2 q^{90} + 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3332, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3332.1.m.a \(2\) \(1.663\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-iq^{2}-q^{4}+(-1-i)q^{5}+iq^{8}+\cdots\)
3332.1.m.b \(2\) \(1.663\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{2}-q^{4}+(1+i)q^{5}-iq^{8}+iq^{9}+\cdots\)
3332.1.m.c \(2\) \(1.663\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q-iq^{2}-q^{4}+(1+i)q^{5}+iq^{8}+iq^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3332, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3332, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 3}\)