Properties

Label 2160.2.q
Level $2160$
Weight $2$
Character orbit 2160.q
Rep. character $\chi_{2160}(721,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $48$
Newform subspaces $12$
Sturm bound $864$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2160.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 12 \)
Sturm bound: \(864\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

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

Total New Old
Modular forms 936 48 888
Cusp forms 792 48 744
Eisenstein series 144 0 144

Trace form

\( 48 q + O(q^{10}) \) \( 48 q - 8 q^{17} - 12 q^{23} - 24 q^{25} + 4 q^{29} - 12 q^{31} - 24 q^{35} - 4 q^{41} - 12 q^{43} - 20 q^{47} - 24 q^{49} + 12 q^{59} + 24 q^{71} + 24 q^{73} + 16 q^{77} + 56 q^{83} + 24 q^{89} + 24 q^{91} - 16 q^{95} - 12 q^{97} + O(q^{100}) \)

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.q.a 2160.q 9.c $2$ $17.248$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+(2-2\zeta_{6})q^{11}+\cdots\)
2160.2.q.b 2160.q 9.c $2$ $17.248$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
2160.2.q.c 2160.q 9.c $2$ $17.248$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{5}+(5-5\zeta_{6})q^{11}-3q^{17}-5q^{19}+\cdots\)
2160.2.q.d 2160.q 9.c $2$ $17.248$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
2160.2.q.e 2160.q 9.c $2$ $17.248$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+4\zeta_{6}q^{13}+\cdots\)
2160.2.q.f 2160.q 9.c $4$ $17.248$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(0\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1})q^{5}+\beta _{3}q^{7}+(\beta _{1}+\beta _{3})q^{11}+\cdots\)
2160.2.q.g 2160.q 9.c $4$ $17.248$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1})q^{5}+(\beta _{1}-\beta _{2})q^{7}+2q^{17}+\cdots\)
2160.2.q.h 2160.q 9.c $4$ $17.248$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{12}q^{5}+(2-2\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{7}+\cdots\)
2160.2.q.i 2160.q 9.c $6$ $17.248$ 6.0.954288.1 None \(0\) \(0\) \(-3\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{2})q^{5}+(-\beta _{2}-\beta _{4})q^{7}+(-\beta _{3}+\cdots)q^{11}+\cdots\)
2160.2.q.j 2160.q 9.c $6$ $17.248$ 6.0.954288.1 None \(0\) \(0\) \(3\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{3})q^{5}+(-\beta _{1}-\beta _{3}+\beta _{4}-\beta _{5})q^{7}+\cdots\)
2160.2.q.k 2160.q 9.c $6$ $17.248$ 6.0.954288.1 None \(0\) \(0\) \(3\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{3})q^{5}+(2\beta _{3}+\beta _{4}-\beta _{5})q^{7}+\cdots\)
2160.2.q.l 2160.q 9.c $8$ $17.248$ 8.0.856615824.2 None \(0\) \(0\) \(4\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1})q^{5}-\beta _{3}q^{7}+(\beta _{3}-\beta _{7})q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2160, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)