Properties

Label 2160.3.e
Level $2160$
Weight $3$
Character orbit 2160.e
Rep. character $\chi_{2160}(271,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $7$
Sturm bound $1296$
Trace bound $37$

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Defining parameters

Level: \( N \) \(=\) \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2160.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(1296\)
Trace bound: \(37\)
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 64 836
Cusp forms 828 64 764
Eisenstein series 72 0 72

Trace form

\( 64 q + O(q^{10}) \) \( 64 q + 16 q^{13} + 320 q^{25} + 80 q^{37} - 464 q^{49} - 112 q^{61} - 80 q^{73} + 112 q^{97} + O(q^{100}) \)

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.e.a 2160.e 4.b $4$ $58.856$ \(\Q(\sqrt{-3}, \sqrt{5})\) None 2160.3.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{5}+2\beta _{2}q^{11}-8q^{13}+3\beta _{1}q^{17}+\cdots\)
2160.3.e.b 2160.e 4.b $4$ $58.856$ \(\Q(\sqrt{-3}, \sqrt{5})\) None 2160.3.e.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{5}+2\beta _{3}q^{7}+4\beta _{2}q^{11}+22q^{13}+\cdots\)
2160.3.e.c 2160.e 4.b $8$ $58.856$ 8.0.121550625.1 None 2160.3.e.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{5}+(\beta _{2}-\beta _{7})q^{7}+(2\beta _{4}-\beta _{5}+\cdots)q^{11}+\cdots\)
2160.3.e.d 2160.e 4.b $12$ $58.856$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 2160.3.e.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{5}-\beta _{2}q^{7}-\beta _{10}q^{11}+(-1+\cdots)q^{13}+\cdots\)
2160.3.e.e 2160.e 4.b $12$ $58.856$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 2160.3.e.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{5}-\beta _{2}q^{7}+\beta _{10}q^{11}+(-1+\cdots)q^{13}+\cdots\)
2160.3.e.f 2160.e 4.b $12$ $58.856$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 2160.3.e.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{5}-\beta _{7}q^{7}+\beta _{9}q^{11}+(1+\beta _{3}+\cdots)q^{13}+\cdots\)
2160.3.e.g 2160.e 4.b $12$ $58.856$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 2160.3.e.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{5}+(\beta _{3}-\beta _{8})q^{7}+\beta _{10}q^{11}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(2160, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)