Properties

Label 2160.3.c
Level $2160$
Weight $3$
Character orbit 2160.c
Rep. character $\chi_{2160}(1889,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $17$
Sturm bound $1296$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2160.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 17 \)
Sturm bound: \(1296\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2160, [\chi])\).

Total New Old
Modular forms 900 96 804
Cusp forms 828 96 732
Eisenstein series 72 0 72

Trace form

\( 96 q + O(q^{10}) \) \( 96 q + 16 q^{19} - 8 q^{25} + 32 q^{31} - 752 q^{49} - 16 q^{55} - 336 q^{61} - 32 q^{79} - 240 q^{85} - 192 q^{91} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2160, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2160.3.c.a 2160.c 15.d $2$ $58.856$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-15}) \) 135.3.d.c \(0\) \(0\) \(-10\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-5q^{5}+(-7-\beta )q^{17}+(-11+\beta )q^{19}+\cdots\)
2160.3.c.b 2160.c 15.d $2$ $58.856$ \(\Q(\sqrt{-1}) \) None 135.3.d.b \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-4-i)q^{5}+2iq^{7}+7iq^{11}+5iq^{13}+\cdots\)
2160.3.c.c 2160.c 15.d $2$ $58.856$ \(\Q(\sqrt{-11}) \) None 135.3.d.a \(0\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{5}+(1-2\beta )q^{7}+(1-2\beta )q^{11}+\cdots\)
2160.3.c.d 2160.c 15.d $2$ $58.856$ \(\Q(\sqrt{-11}) \) None 135.3.d.a \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{5}+(1-2\beta )q^{7}+(-1+2\beta )q^{11}+\cdots\)
2160.3.c.e 2160.c 15.d $2$ $58.856$ \(\Q(\sqrt{-1}) \) None 135.3.d.b \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(4+i)q^{5}+2iq^{7}-7iq^{11}+5iq^{13}+\cdots\)
2160.3.c.f 2160.c 15.d $2$ $58.856$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-15}) \) 135.3.d.c \(0\) \(0\) \(10\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+5q^{5}+(7+\beta )q^{17}+(-11+\beta )q^{19}+\cdots\)
2160.3.c.g 2160.c 15.d $4$ $58.856$ 4.0.31744.1 None 270.3.b.a \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-3-\beta _{1}-\beta _{2})q^{5}+(\beta _{1}+2\beta _{3})q^{7}+\cdots\)
2160.3.c.h 2160.c 15.d $4$ $58.856$ \(\Q(\sqrt{-11}, \sqrt{-19})\) None 540.3.b.a \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{1})q^{5}-\beta _{2}q^{7}+(-2\beta _{1}-3\beta _{2}+\cdots)q^{11}+\cdots\)
2160.3.c.i 2160.c 15.d $4$ $58.856$ \(\Q(\zeta_{8})\) None 270.3.b.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+5\zeta_{8}^{3}q^{5}+5\zeta_{8}^{2}q^{7}+(\zeta_{8}+\zeta_{8}^{3})q^{11}+\cdots\)
2160.3.c.j 2160.c 15.d $4$ $58.856$ \(\Q(\zeta_{8})\) None 270.3.b.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(4\zeta_{8}-3\zeta_{8}^{3})q^{5}-11\zeta_{8}^{2}q^{7}+(5\zeta_{8}+\cdots)q^{11}+\cdots\)
2160.3.c.k 2160.c 15.d $4$ $58.856$ \(\Q(i, \sqrt{10})\) None 135.3.d.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{2}+\beta _{3})q^{5}+\beta _{1}q^{7}+(-2\beta _{2}+\cdots)q^{11}+\cdots\)
2160.3.c.l 2160.c 15.d $4$ $58.856$ \(\Q(\sqrt{-11}, \sqrt{-19})\) None 540.3.b.a \(0\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{1})q^{5}-\beta _{2}q^{7}+(2\beta _{1}+3\beta _{2}+\cdots)q^{11}+\cdots\)
2160.3.c.m 2160.c 15.d $4$ $58.856$ 4.0.31744.1 None 270.3.b.a \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(3+\beta _{1}+\beta _{2})q^{5}+(\beta _{1}+2\beta _{3})q^{7}+\cdots\)
2160.3.c.n 2160.c 15.d $8$ $58.856$ 8.0.\(\cdots\).13 None 540.3.b.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{5}+(-\beta _{1}-\beta _{3})q^{7}-\beta _{6}q^{11}+\cdots\)
2160.3.c.o 2160.c 15.d $12$ $58.856$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 1080.3.c.a \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{5}-\beta _{5}q^{7}+\beta _{9}q^{11}+\beta _{8}q^{13}+\cdots\)
2160.3.c.p 2160.c 15.d $12$ $58.856$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 1080.3.c.a \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{5}-\beta _{5}q^{7}-\beta _{9}q^{11}+\beta _{8}q^{13}+\cdots\)
2160.3.c.q 2160.c 15.d $24$ $58.856$ None 1080.3.c.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(2160, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2160, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)