Properties

Label 1620.3.t
Level $1620$
Weight $3$
Character orbit 1620.t
Rep. character $\chi_{1620}(269,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $6$
Sturm bound $972$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1620.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(972\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(17\)

Dimensions

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

Total New Old
Modular forms 1368 96 1272
Cusp forms 1224 96 1128
Eisenstein series 144 0 144

Trace form

\( 96 q + O(q^{10}) \) \( 96 q - 6 q^{25} - 60 q^{31} + 288 q^{49} - 12 q^{55} - 96 q^{61} - 588 q^{79} - 24 q^{85} + 168 q^{91} + O(q^{100}) \)

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.t.a 1620.t 45.h $8$ $44.142$ 8.0.\(\cdots\).1 None \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}-\beta _{7})q^{5}+\beta _{1}q^{7}+(-3\beta _{1}-2\beta _{4}+\cdots)q^{11}+\cdots\)
1620.3.t.b 1620.t 45.h $8$ $44.142$ 8.0.12960000.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{5}q^{5}-2\beta _{4}q^{7}+(\beta _{2}+2\beta _{5}+2\beta _{6}+\cdots)q^{11}+\cdots\)
1620.3.t.c 1620.t 45.h $8$ $44.142$ 8.0.\(\cdots\).6 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}+\beta _{5}+\beta _{6})q^{5}+\beta _{3}q^{7}-7\beta _{4}q^{11}+\cdots\)
1620.3.t.d 1620.t 45.h $8$ $44.142$ 8.0.\(\cdots\).1 None \(0\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{2}+\beta _{7})q^{5}+\beta _{1}q^{7}+(3\beta _{1}+2\beta _{4}+\cdots)q^{11}+\cdots\)
1620.3.t.e 1620.t 45.h $16$ $44.142$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{4}q^{5}+(-\beta _{3}+\beta _{7})q^{7}+\beta _{14}q^{11}+\cdots\)
1620.3.t.f 1620.t 45.h $48$ $44.142$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

\( S_{3}^{\mathrm{old}}(1620, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(810, [\chi])\)\(^{\oplus 2}\)