Properties

Label 2160.2.x
Level $2160$
Weight $2$
Character orbit 2160.x
Rep. character $\chi_{2160}(703,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $96$
Newform subspaces $7$
Sturm bound $864$
Trace bound $13$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2160.x (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 7 \)
Sturm bound: \(864\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2160, [\chi])\).

Total New Old
Modular forms 936 96 840
Cusp forms 792 96 696
Eisenstein series 144 0 144

Trace form

\( 96 q + O(q^{10}) \) \( 96 q - 96 q^{37} - 24 q^{73} + 96 q^{85} - 24 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2160, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2160.2.x.a 2160.x 20.e $8$ $17.248$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+2\zeta_{24}^{3})q^{5}+(-\zeta_{24}^{4}-\zeta_{24}^{6}+\cdots)q^{7}+\cdots\)
2160.2.x.b 2160.x 20.e $8$ $17.248$ 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{4}q^{5}+(-\beta _{3}+\beta _{5})q^{11}+(-2+2\beta _{2}+\cdots)q^{13}+\cdots\)
2160.2.x.c 2160.x 20.e $8$ $17.248$ 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{5}+(-\beta _{4}+\beta _{5})q^{7}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)
2160.2.x.d 2160.x 20.e $8$ $17.248$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-2\zeta_{24}^{3})q^{5}+(-\zeta_{24}^{4}-\zeta_{24}^{6}+\cdots)q^{7}+\cdots\)
2160.2.x.e 2160.x 20.e $16$ $17.248$ 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{5}+(-\beta _{2}-\beta _{6}+\beta _{7})q^{7}+\beta _{13}q^{11}+\cdots\)
2160.2.x.f 2160.x 20.e $16$ $17.248$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\beta _{6}+\beta _{15})q^{5}+(-\beta _{1}+\beta _{5}-\beta _{8}+\cdots)q^{7}+\cdots\)
2160.2.x.g 2160.x 20.e $32$ $17.248$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2160, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2160, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)