Properties

Label 2624.1.h
Level $2624$
Weight $1$
Character orbit 2624.h
Rep. character $\chi_{2624}(2623,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $3$
Sturm bound $336$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 2624 = 2^{6} \cdot 41 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2624.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 164 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(336\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2624, [\chi])\).

Total New Old
Modular forms 46 9 37
Cusp forms 34 7 27
Eisenstein series 12 2 10

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 7 0 0 0

Trace form

\( 7 q + 2 q^{5} + 5 q^{9} + O(q^{10}) \) \( 7 q + 2 q^{5} + 5 q^{9} + 4 q^{21} + 5 q^{25} - 4 q^{33} + 2 q^{37} - q^{41} + 6 q^{45} + 5 q^{49} - 4 q^{57} + 2 q^{61} - 2 q^{73} + 4 q^{77} + 3 q^{81} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2624, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2624.1.h.a \(1\) \(1.310\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-41}) \) \(\Q(\sqrt{41}) \) \(0\) \(0\) \(2\) \(0\) \(q+2q^{5}-q^{9}+3q^{25}+2q^{37}+q^{41}+\cdots\)
2624.1.h.b \(2\) \(1.310\) \(\Q(\sqrt{2}) \) \(D_{4}\) \(\Q(\sqrt{-41}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{3}-\beta q^{7}+q^{9}+\beta q^{11}-\beta q^{19}+\cdots\)
2624.1.h.c \(4\) \(1.310\) \(\Q(\zeta_{16})^+\) \(D_{8}\) \(\Q(\sqrt{-41}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}+(1-\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2624, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2624, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(164, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(656, [\chi])\)\(^{\oplus 3}\)