Properties

Label 1620.2.d
Level $1620$
Weight $2$
Character orbit 1620.d
Rep. character $\chi_{1620}(649,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $5$
Sturm bound $648$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1620.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(648\)
Trace bound: \(5\)
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 360 24 336
Cusp forms 288 24 264
Eisenstein series 72 0 72

Trace form

\( 24 q + O(q^{10}) \) \( 24 q - 12 q^{31} - 36 q^{49} + 30 q^{55} - 24 q^{61} - 36 q^{79} + 30 q^{85} + 36 q^{91} + O(q^{100}) \)

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.d.a \(2\) \(12.936\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-i)q^{5}+iq^{7}+q^{11}-iq^{17}+\cdots\)
1620.2.d.b \(2\) \(12.936\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1+i)q^{5}+iq^{7}-q^{11}+iq^{17}+\cdots\)
1620.2.d.c \(6\) \(12.936\) 6.0.301925376.2 None \(0\) \(0\) \(-1\) \(0\) \(q+\beta _{3}q^{5}+(\beta _{1}+\beta _{3}-\beta _{4})q^{7}-\beta _{2}q^{11}+\cdots\)
1620.2.d.d \(6\) \(12.936\) 6.0.301925376.2 None \(0\) \(0\) \(1\) \(0\) \(q-\beta _{3}q^{5}+(\beta _{1}+\beta _{3}-\beta _{4})q^{7}+\beta _{2}q^{11}+\cdots\)
1620.2.d.e \(8\) \(12.936\) 8.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{5}-\beta _{2}q^{7}+(-\beta _{1}+\beta _{4}+\beta _{6}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1620, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(810, [\chi])\)\(^{\oplus 2}\)