Properties

Label 960.2.k
Level $960$
Weight $2$
Character orbit 960.k
Rep. character $\chi_{960}(481,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $6$
Sturm bound $384$
Trace bound $15$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 960.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(384\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(7\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(960, [\chi])\).

Total New Old
Modular forms 216 16 200
Cusp forms 168 16 152
Eisenstein series 48 0 48

Trace form

\( 16 q - 16 q^{9} + O(q^{10}) \) \( 16 q - 16 q^{9} - 16 q^{25} - 16 q^{49} + 32 q^{57} + 32 q^{73} + 16 q^{81} - 32 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(960, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
960.2.k.a 960.k 8.b $2$ $7.666$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}-iq^{5}-4q^{7}-q^{9}-4iq^{11}+\cdots\)
960.2.k.b 960.k 8.b $2$ $7.666$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}-iq^{5}-q^{9}-6iq^{13}-q^{15}+\cdots\)
960.2.k.c 960.k 8.b $2$ $7.666$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-iq^{5}-q^{9}-6iq^{13}+q^{15}+\cdots\)
960.2.k.d 960.k 8.b $2$ $7.666$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-iq^{5}+4q^{7}-q^{9}+4iq^{11}+\cdots\)
960.2.k.e 960.k 8.b $4$ $7.666$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}q^{3}+\zeta_{12}q^{5}-2q^{7}-q^{9}+(2\zeta_{12}+\cdots)q^{11}+\cdots\)
960.2.k.f 960.k 8.b $4$ $7.666$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}q^{3}+\zeta_{12}q^{5}+2q^{7}-q^{9}+(-2\zeta_{12}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(960, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)