Properties

Label 72.7.e
Level $72$
Weight $7$
Character orbit 72.e
Rep. character $\chi_{72}(17,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $2$
Sturm bound $84$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 7 \)
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: \(84\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(72, [\chi])\).

Total New Old
Modular forms 80 6 74
Cusp forms 64 6 58
Eisenstein series 16 0 16

Trace form

\( 6 q - 312 q^{7} + O(q^{10}) \) \( 6 q - 312 q^{7} - 1968 q^{13} - 10080 q^{19} - 78390 q^{25} + 37608 q^{31} - 215148 q^{37} + 121680 q^{43} - 317958 q^{49} + 1102320 q^{55} - 532980 q^{61} + 1250160 q^{67} - 521184 q^{73} + 1416792 q^{79} - 66180 q^{85} - 1725504 q^{91} + 5472 q^{97} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(72, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
72.7.e.a 72.e 3.b $2$ $16.564$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(120\) $\mathrm{SU}(2)[C_{2}]$ \(q+5\beta q^{5}+60q^{7}+236\beta q^{11}+1192q^{13}+\cdots\)
72.7.e.b 72.e 3.b $4$ $16.564$ \(\Q(\sqrt{-2}, \sqrt{145})\) None \(0\) \(0\) \(0\) \(-432\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-5^{2}\beta _{1}-\beta _{3})q^{5}+(-108-\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(72, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(72, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)