Properties

Label 1620.2.i
Level $1620$
Weight $2$
Character orbit 1620.i
Rep. character $\chi_{1620}(541,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $32$
Newform subspaces $14$
Sturm bound $648$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1620.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 14 \)
Sturm bound: \(648\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\)

Dimensions

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

Total New Old
Modular forms 720 32 688
Cusp forms 576 32 544
Eisenstein series 144 0 144

Trace form

\( 32q + 10q^{7} + O(q^{10}) \) \( 32q + 10q^{7} + 10q^{13} - 44q^{19} - 16q^{25} - 20q^{31} - 20q^{37} - 8q^{43} + 6q^{49} + 10q^{61} + 10q^{67} - 20q^{73} - 2q^{79} - 12q^{85} + 68q^{91} + 22q^{97} + O(q^{100}) \)

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.i.a \(2\) \(12.936\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-2\) \(q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots\)
1620.2.i.b \(2\) \(12.936\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-2\) \(q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots\)
1620.2.i.c \(2\) \(12.936\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-2\) \(q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
1620.2.i.d \(2\) \(12.936\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(1\) \(q-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
1620.2.i.e \(2\) \(12.936\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(4\) \(q-\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
1620.2.i.f \(2\) \(12.936\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(4\) \(q-\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
1620.2.i.g \(2\) \(12.936\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(-2\) \(q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
1620.2.i.h \(2\) \(12.936\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(-2\) \(q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots\)
1620.2.i.i \(2\) \(12.936\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(-2\) \(q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots\)
1620.2.i.j \(2\) \(12.936\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(1\) \(q+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
1620.2.i.k \(2\) \(12.936\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(4\) \(q+\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
1620.2.i.l \(2\) \(12.936\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(4\) \(q+\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
1620.2.i.m \(4\) \(12.936\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(2\) \(q+(-1+\zeta_{12})q^{5}+(\zeta_{12}-\zeta_{12}^{2})q^{7}+\cdots\)
1620.2.i.n \(4\) \(12.936\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(2\) \(q+(1-\zeta_{12})q^{5}+(\zeta_{12}-\zeta_{12}^{2})q^{7}+\zeta_{12}^{2}q^{11}+\cdots\)

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

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