Properties

Label 2160.2.f
Level $2160$
Weight $2$
Character orbit 2160.f
Rep. character $\chi_{2160}(1729,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $15$
Sturm bound $864$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2160.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(864\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\)

Dimensions

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

Total New Old
Modular forms 468 48 420
Cusp forms 396 48 348
Eisenstein series 72 0 72

Trace form

\( 48 q + O(q^{10}) \) \( 48 q - 4 q^{19} - 4 q^{25} + 4 q^{31} - 40 q^{49} - 20 q^{55} + 24 q^{61} + 20 q^{79} - 24 q^{85} - 24 q^{91} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2160.2.f.a 2160.f 5.b $2$ $17.248$ \(\Q(\sqrt{-1}) \) None 540.2.d.a \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2+i)q^{5}+2iq^{7}-2q^{11}-6iq^{13}+\cdots\)
2160.2.f.b 2160.f 5.b $2$ $17.248$ \(\Q(\sqrt{-1}) \) None 1080.2.f.a \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2-i)q^{5}+2iq^{7}+2q^{11}-2iq^{13}+\cdots\)
2160.2.f.c 2160.f 5.b $2$ $17.248$ \(\Q(\sqrt{-1}) \) None 1080.2.f.b \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+2i)q^{5}+4iq^{7}+q^{11}-iq^{13}+\cdots\)
2160.2.f.d 2160.f 5.b $2$ $17.248$ \(\Q(\sqrt{-1}) \) None 270.2.c.a \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-2i)q^{5}+4iq^{7}+5q^{11}-3iq^{13}+\cdots\)
2160.2.f.e 2160.f 5.b $2$ $17.248$ \(\Q(\sqrt{-1}) \) None 270.2.c.a \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+2i)q^{5}+4iq^{7}-5q^{11}-3iq^{13}+\cdots\)
2160.2.f.f 2160.f 5.b $2$ $17.248$ \(\Q(\sqrt{-1}) \) None 1080.2.f.b \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-2i)q^{5}+4iq^{7}-q^{11}-iq^{13}+\cdots\)
2160.2.f.g 2160.f 5.b $2$ $17.248$ \(\Q(\sqrt{-1}) \) None 1080.2.f.a \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2+i)q^{5}+2iq^{7}-2q^{11}-2iq^{13}+\cdots\)
2160.2.f.h 2160.f 5.b $2$ $17.248$ \(\Q(\sqrt{-1}) \) None 540.2.d.a \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2-i)q^{5}+2iq^{7}+2q^{11}-6iq^{13}+\cdots\)
2160.2.f.i 2160.f 5.b $4$ $17.248$ \(\Q(i, \sqrt{6})\) None 1080.2.f.e \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{1}+\beta _{2})q^{5}-\beta _{2}q^{7}+(-2+\cdots)q^{11}+\cdots\)
2160.2.f.j 2160.f 5.b $4$ $17.248$ \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-15}) \) 135.2.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{5}+(-\beta _{1}-2\beta _{2})q^{17}+(-2+\cdots)q^{19}+\cdots\)
2160.2.f.k 2160.f 5.b $4$ $17.248$ \(\Q(\zeta_{8})\) None 135.2.b.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{3}q^{5}+\zeta_{8}q^{7}+(-\zeta_{8}^{2}+2\zeta_{8}^{3})q^{11}+\cdots\)
2160.2.f.l 2160.f 5.b $4$ $17.248$ \(\Q(i, \sqrt{10})\) None 540.2.d.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{5}+\beta _{2}q^{7}+(-\beta _{1}+\beta _{3})q^{11}+\cdots\)
2160.2.f.m 2160.f 5.b $4$ $17.248$ \(\Q(i, \sqrt{19})\) None 270.2.c.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{5}+(-1-2\beta _{3})q^{7}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)
2160.2.f.n 2160.f 5.b $4$ $17.248$ \(\Q(i, \sqrt{6})\) None 1080.2.f.e \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{2}+\beta _{3})q^{5}+\beta _{2}q^{7}+(2+\beta _{1}+\cdots)q^{11}+\cdots\)
2160.2.f.o 2160.f 5.b $8$ $17.248$ 8.0.2702336256.1 None 1080.2.f.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{7}q^{5}-\beta _{1}q^{7}+(-2\beta _{3}-\beta _{6}+2\beta _{7})q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2160, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)