Properties

Label 72.3.e
Level $72$
Weight $3$
Character orbit 72.e
Rep. character $\chi_{72}(17,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $36$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 72.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(72, [\chi])\).

Total New Old
Modular forms 32 2 30
Cusp forms 16 2 14
Eisenstein series 16 0 16

Trace form

\( 2q + 24q^{7} + O(q^{10}) \) \( 2q + 24q^{7} - 16q^{13} - 32q^{19} - 50q^{25} - 8q^{31} + 60q^{37} - 16q^{43} + 190q^{49} + 80q^{55} - 28q^{61} - 176q^{67} - 160q^{73} + 200q^{79} - 140q^{85} - 192q^{91} - 224q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(72, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
72.3.e.a \(2\) \(1.962\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(24\) \(q+5\beta q^{5}+12q^{7}-4\beta q^{11}-8q^{13}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(72, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(72, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)