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Properties

Label 1488.1.br
Level $1488$
Weight $1$
Character orbit 1488.br
Rep. character $\chi_{1488}(593,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $4$
Newform subspaces $1$
Sturm bound $256$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1488 = 2^{4} \cdot 3 \cdot 31 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1488.br (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 93 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(256\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1488, [\chi])\).

Total New Old
Modular forms 72 12 60
Cusp forms 24 4 20
Eisenstein series 48 8 40

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q + q^{3} + 2 q^{7} - q^{9} - 2 q^{13} + 2 q^{19} + 3 q^{21} + 4 q^{25} + q^{27} + q^{31} - 2 q^{37} - 3 q^{39} - 3 q^{43} - 3 q^{49} - 2 q^{57} - 2 q^{61} + 2 q^{63} + 2 q^{67} - 2 q^{73} + q^{75}+ \cdots + 3 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(1488, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1488.1.br.a 1488.br 93.l $4$ $0.743$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-3}) \) None 93.1.l.a \(0\) \(1\) \(0\) \(2\) \(q-\zeta_{10}^{4}q^{3}+(\zeta_{10}+\zeta_{10}^{3})q^{7}-\zeta_{10}^{3}q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1488, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1488, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 5}\)