Properties

Label 1620.2.r
Level $1620$
Weight $2$
Character orbit 1620.r
Rep. character $\chi_{1620}(109,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $8$
Sturm bound $648$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1620.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 8 \)
Sturm bound: \(648\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1620, [\chi])\).

Total New Old
Modular forms 720 48 672
Cusp forms 576 48 528
Eisenstein series 144 0 144

Trace form

\( 48 q + O(q^{10}) \) \( 48 q + 6 q^{25} - 12 q^{31} + 36 q^{49} + 48 q^{55} - 12 q^{61} + 48 q^{79} + 6 q^{85} - 24 q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1620, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1620.2.r.a \(4\) \(12.936\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) \(q+(-\zeta_{12}-2\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+2\zeta_{12}q^{7}+\cdots\)
1620.2.r.b \(4\) \(12.936\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(0\) \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+\zeta_{12}q^{7}+\cdots\)
1620.2.r.c \(4\) \(12.936\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{5}+2\zeta_{12}q^{7}+\cdots\)
1620.2.r.d \(4\) \(12.936\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+2\zeta_{12}q^{7}+\cdots\)
1620.2.r.e \(4\) \(12.936\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(0\) \(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{5}+\zeta_{12}q^{7}+\cdots\)
1620.2.r.f \(4\) \(12.936\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(0\) \(q+(\zeta_{12}+2\zeta_{12}^{2}-\zeta_{12}^{3})q^{5}+2\zeta_{12}q^{7}+\cdots\)
1620.2.r.g \(8\) \(12.936\) 8.0.3317760000.2 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{3}+\beta _{7})q^{5}+(\beta _{2}-\beta _{6})q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
1620.2.r.h \(16\) \(12.936\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{14}q^{5}+(\beta _{2}-\beta _{12})q^{7}+(-\beta _{1}-\beta _{4}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1620, [\chi])\) into lower level spaces

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