Properties

Label 3888.1.q
Level $3888$
Weight $1$
Character orbit 3888.q
Rep. character $\chi_{3888}(161,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $10$
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.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
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 164 10 154
Cusp forms 56 10 46
Eisenstein series 108 0 108

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 4 0

Trace form

\( 10 q - 2 q^{13} + 4 q^{19} - q^{25} - 5 q^{31} - q^{43} - q^{49} + 8 q^{55} - 2 q^{61} - 2 q^{67} + 4 q^{73} + 2 q^{79} - 4 q^{85} + 6 q^{91} + 2 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3888.1.q.a 3888.q 9.d $2$ $1.940$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-3}) \) None 972.1.c.a \(0\) \(0\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{7}-\zeta_{6}q^{13}-q^{19}+\zeta_{6}^{2}q^{25}+\cdots\)
3888.1.q.b 3888.q 9.d $2$ $1.940$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-3}) \) None 243.1.b.a \(0\) \(0\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{7}+\zeta_{6}q^{13}+q^{19}+\zeta_{6}^{2}q^{25}+\cdots\)
3888.1.q.c 3888.q 9.d $2$ $1.940$ \(\Q(\sqrt{-3}) \) $D_{3}$ \(\Q(\sqrt{-3}) \) None 972.1.c.b \(0\) \(0\) \(0\) \(2\) \(q-\zeta_{6}^{2}q^{7}+\zeta_{6}q^{13}+q^{19}+\zeta_{6}^{2}q^{25}+\cdots\)
3888.1.q.d 3888.q 9.d $4$ $1.940$ \(\Q(\sqrt{-2}, \sqrt{-3})\) $S_{4}$ None None 1944.1.e.a \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{3})q^{5}-\beta _{1}q^{11}-\beta _{2}q^{13}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3888, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(243, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(972, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1296, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1944, [\chi])\)\(^{\oplus 2}\)