Properties

Label 3888.1.e
Level $3888$
Weight $1$
Character orbit 3888.e
Rep. character $\chi_{3888}(1457,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $4$
Sturm bound $648$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 3888 = 2^{4} \cdot 3^{5} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3888.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(648\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3888, [\chi])\).

Total New Old
Modular forms 86 5 81
Cusp forms 32 5 27
Eisenstein series 54 0 54

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 3 0 2 0

Trace form

\( 5 q + O(q^{10}) \) \( 5 q + 2 q^{13} + 2 q^{19} + q^{25} + 5 q^{31} + q^{43} + q^{49} + 4 q^{55} + 2 q^{61} + 2 q^{67} + 2 q^{73} - 2 q^{79} + 4 q^{85} + 3 q^{91} - 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3888, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3888.1.e.a 3888.e 3.b $1$ $1.940$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-2q^{7}-q^{13}+q^{19}+q^{25}+q^{31}+\cdots\)
3888.1.e.b 3888.e 3.b $1$ $1.940$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+q^{7}-q^{13}+q^{19}+q^{25}+q^{31}+\cdots\)
3888.1.e.c 3888.e 3.b $1$ $1.940$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+q^{7}+2q^{13}-2q^{19}+q^{25}+q^{31}+\cdots\)
3888.1.e.d 3888.e 3.b $2$ $1.940$ \(\Q(\sqrt{-2}) \) $S_{4}$ None None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{5}-\beta q^{11}+q^{13}-\beta q^{17}+q^{19}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3888, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3888, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(243, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(972, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1944, [\chi])\)\(^{\oplus 2}\)