Properties

Label 416.1.h
Level $416$
Weight $1$
Character orbit 416.h
Rep. character $\chi_{416}(207,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $56$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 416 = 2^{5} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 416.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 104 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(56\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(416, [\chi])\).

Total New Old
Modular forms 16 4 12
Cusp forms 8 2 6
Eisenstein series 8 2 6

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

\( 2q + 2q^{3} + O(q^{10}) \) \( 2q + 2q^{3} - 2q^{17} - 2q^{27} - 2q^{35} + 2q^{43} - 2q^{51} - 2q^{65} - 2q^{81} + 2q^{91} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(416, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
416.1.h.a \(1\) \(0.208\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-26}) \) None \(0\) \(1\) \(-1\) \(1\) \(q+q^{3}-q^{5}+q^{7}+q^{13}-q^{15}-q^{17}+\cdots\)
416.1.h.b \(1\) \(0.208\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-26}) \) None \(0\) \(1\) \(1\) \(-1\) \(q+q^{3}+q^{5}-q^{7}-q^{13}+q^{15}-q^{17}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(416, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(416, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 3}\)