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Properties

Label 1425.1.t
Level $1425$
Weight $1$
Character orbit 1425.t
Rep. character $\chi_{1425}(26,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $6$
Newform subspaces $2$
Sturm bound $200$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1425 = 3 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1425.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(200\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1425, [\chi])\).

Total New Old
Modular forms 36 18 18
Cusp forms 12 6 6
Eisenstein series 24 12 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

\( 6 q + q^{3} - q^{4} + 2 q^{6} + 2 q^{7} + q^{9} + O(q^{10}) \) \( 6 q + q^{3} - q^{4} + 2 q^{6} + 2 q^{7} + q^{9} - 2 q^{12} - q^{13} + q^{16} + 4 q^{19} + q^{21} + 2 q^{24} - 2 q^{27} - q^{28} - 6 q^{31} + 2 q^{34} - q^{36} + 2 q^{37} - 2 q^{39} - q^{43} - 8 q^{46} + q^{48} - 4 q^{49} + 2 q^{51} - q^{52} - 2 q^{54} + q^{57} - 3 q^{61} - q^{63} - 2 q^{64} - q^{67} - 8 q^{69} - q^{73} - q^{76} + 5 q^{79} - 3 q^{81} - 2 q^{84} - q^{91} - q^{93} - 4 q^{94} + 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(1425, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1425.1.t.a 1425.t 57.h $2$ $0.711$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-3}) \) None 57.1.h.a \(0\) \(1\) \(0\) \(2\) \(q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+q^{7}-\zeta_{6}q^{9}-q^{12}+\cdots\)
1425.1.t.b 1425.t 57.h $4$ $0.711$ \(\Q(\zeta_{12})\) $D_{3}$ \(\Q(\sqrt{-15}) \) None 285.1.n.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{6}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1425, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1425, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 3}\)