Properties

Label 3328.1.c
Level $3328$
Weight $1$
Character orbit 3328.c
Rep. character $\chi_{3328}(3327,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $6$
Sturm bound $448$
Trace bound $13$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3328 = 2^{8} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3328.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 52 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(448\)
Trace bound: \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3328, [\chi])\).

Total New Old
Modular forms 46 18 28
Cusp forms 22 14 8
Eisenstein series 24 4 20

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 14 0 0 0

Trace form

\( 14 q - 2 q^{9} + O(q^{10}) \) \( 14 q - 2 q^{9} - 4 q^{17} - 2 q^{25} + 10 q^{49} - 4 q^{65} + 6 q^{81} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3328, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3328.1.c.a 3328.c 52.b $2$ $1.661$ \(\Q(\sqrt{-1}) \) $D_{3}$ \(\Q(\sqrt{-26}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-iq^{3}-iq^{5}-q^{7}-iq^{13}-q^{15}+\cdots\)
3328.1.c.b 3328.c 52.b $2$ $1.661$ \(\Q(\sqrt{2}) \) $D_{4}$ \(\Q(\sqrt{-13}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{7}+q^{9}-\beta q^{11}-q^{13}+\beta q^{19}+\cdots\)
3328.1.c.c 3328.c 52.b $2$ $1.661$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-26}) \) \(\Q(\sqrt{26}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{5}+q^{9}-iq^{13}+q^{17}-3q^{25}+\cdots\)
3328.1.c.d 3328.c 52.b $2$ $1.661$ \(\Q(\sqrt{2}) \) $D_{4}$ \(\Q(\sqrt{-13}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{7}+q^{9}-\beta q^{11}+q^{13}+\beta q^{19}+\cdots\)
3328.1.c.e 3328.c 52.b $2$ $1.661$ \(\Q(\sqrt{-1}) \) $D_{3}$ \(\Q(\sqrt{-26}) \) None \(0\) \(0\) \(0\) \(2\) \(q+iq^{3}-iq^{5}+q^{7}-iq^{13}+q^{15}+\cdots\)
3328.1.c.f 3328.c 52.b $4$ $1.661$ \(\Q(\zeta_{12})\) $D_{6}$ \(\Q(\sqrt{-26}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{3}-\zeta_{12}^{3}q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3328, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3328, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(832, [\chi])\)\(^{\oplus 3}\)