Properties

Label 1407.1.cz
Level $1407$
Weight $1$
Character orbit 1407.cz
Rep. character $\chi_{1407}(23,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $20$
Newform subspaces $1$
Sturm bound $181$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1407 = 3 \cdot 7 \cdot 67 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1407.cz (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1407 \)
Character field: \(\Q(\zeta_{66})\)
Newform subspaces: \( 1 \)
Sturm bound: \(181\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1407, [\chi])\).

Total New Old
Modular forms 100 100 0
Cusp forms 20 20 0
Eisenstein series 80 80 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 20 0 0 0

Trace form

\( 20q + q^{3} - 2q^{4} + q^{7} + q^{9} + O(q^{10}) \) \( 20q + q^{3} - 2q^{4} + q^{7} + q^{9} + q^{12} + 2q^{13} - 2q^{16} + 2q^{19} + q^{21} + q^{25} - 2q^{27} + q^{28} - 4q^{31} + q^{36} + 2q^{37} + 2q^{39} - 4q^{43} + q^{48} + q^{49} - 9q^{52} + 21q^{57} + 2q^{61} - 2q^{63} - 2q^{64} + q^{67} - 12q^{73} + q^{75} + 2q^{76} - 12q^{79} + q^{81} - 10q^{84} + 2q^{91} + 2q^{93} - q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1407, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1407.1.cz.a \(20\) \(0.702\) \(\Q(\zeta_{33})\) \(D_{33}\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(1\) \(q+\zeta_{66}^{4}q^{3}-\zeta_{66}^{27}q^{4}-\zeta_{66}^{13}q^{7}+\cdots\)