Properties

Label 1620.3.o
Level $1620$
Weight $3$
Character orbit 1620.o
Rep. character $\chi_{1620}(701,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $7$
Sturm bound $972$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1620.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 7 \)
Sturm bound: \(972\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1620, [\chi])\).

Total New Old
Modular forms 1368 64 1304
Cusp forms 1224 64 1160
Eisenstein series 144 0 144

Trace form

\( 64 q - 10 q^{7} + O(q^{10}) \) \( 64 q - 10 q^{7} + 50 q^{13} + 92 q^{19} + 160 q^{25} + 80 q^{31} - 220 q^{37} - 280 q^{43} - 402 q^{49} + 98 q^{61} + 158 q^{67} - 76 q^{73} + 182 q^{79} - 60 q^{85} - 764 q^{91} - 310 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1620, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1620.3.o.a 1620.o 9.d $4$ $44.142$ \(\Q(\sqrt{-3}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{3})q^{5}+(-8+8\beta _{2})q^{7}-9\beta _{1}q^{11}+\cdots\)
1620.3.o.b 1620.o 9.d $4$ $44.142$ \(\Q(\sqrt{-3}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}+\beta _{3})q^{5}+(-2+2\beta _{2})q^{7}+\cdots\)
1620.3.o.c 1620.o 9.d $4$ $44.142$ \(\Q(\sqrt{-3}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{1}q^{5}+4\beta _{2}q^{7}+(-3\beta _{1}+3\beta _{3})q^{11}+\cdots\)
1620.3.o.d 1620.o 9.d $4$ $44.142$ \(\Q(\sqrt{-3}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(14\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{3})q^{5}+(7-7\beta _{2})q^{7}+6\beta _{1}q^{11}+\cdots\)
1620.3.o.e 1620.o 9.d $8$ $44.142$ 8.0.12960000.1 None \(0\) \(0\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}+\beta _{4})q^{5}+(-5+5\beta _{2}+\beta _{6}+\cdots)q^{7}+\cdots\)
1620.3.o.f 1620.o 9.d $8$ $44.142$ 8.0.3317760000.8 None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{5}+(4-4\beta _{2}-\beta _{7})q^{7}+(-\beta _{4}+\cdots)q^{11}+\cdots\)
1620.3.o.g 1620.o 9.d $32$ $44.142$ None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(1620, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1620, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(810, [\chi])\)\(^{\oplus 2}\)