Properties

Label 960.1.c
Level $960$
Weight $1$
Character orbit 960.c
Rep. character $\chi_{960}(449,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 960.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(960, [\chi])\).

Total New Old
Modular forms 36 8 28
Cusp forms 12 4 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 4 0 0 0

Trace form

\( 4 q + O(q^{10}) \) \( 4 q - 4 q^{21} - 4 q^{25} + 4 q^{45} - 4 q^{49} + 4 q^{69} - 4 q^{81} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(960, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
960.1.c.a 960.c 15.d $4$ $0.479$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{5}+(\zeta_{8}+\zeta_{8}^{3})q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(960, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(960, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)