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Properties

Label 72.5.e
Level $72$
Weight $5$
Character orbit 72.e
Rep. character $\chi_{72}(17,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $60$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 72.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(60\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(72, [\chi])\).

Total New Old
Modular forms 56 4 52
Cusp forms 40 4 36
Eisenstein series 16 0 16

Trace form

\( 4 q - 48 q^{7} + O(q^{10}) \) \( 4 q - 48 q^{7} + 256 q^{13} - 832 q^{19} + 1916 q^{25} - 3184 q^{31} + 3096 q^{37} - 608 q^{43} + 188 q^{49} - 4256 q^{55} - 2072 q^{61} + 19808 q^{67} - 10688 q^{73} - 11792 q^{79} - 17560 q^{85} + 43008 q^{91} + 128 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(72, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
72.5.e.a 72.e 3.b $2$ $7.443$ \(\Q(\sqrt{-2}) \) None 72.5.e.a \(0\) \(0\) \(0\) \(-120\) $\mathrm{SU}(2)[C_{2}]$ \(q+11\beta q^{5}-60q^{7}+44\beta q^{11}-176q^{13}+\cdots\)
72.5.e.b 72.e 3.b $2$ $7.443$ \(\Q(\sqrt{-2}) \) None 72.5.e.b \(0\) \(0\) \(0\) \(72\) $\mathrm{SU}(2)[C_{2}]$ \(q+5\beta q^{5}+6^{2}q^{7}+116\beta q^{11}+304q^{13}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(72, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(72, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)