Properties

Label 72.7.h
Level $72$
Weight $7$
Character orbit 72.h
Rep. character $\chi_{72}(53,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $1$
Sturm bound $84$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 72.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(84\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 76 24 52
Cusp forms 68 24 44
Eisenstein series 8 0 8

Trace form

\( 24 q + 132 q^{4} + O(q^{10}) \) \( 24 q + 132 q^{4} + 588 q^{10} + 4536 q^{16} + 11784 q^{22} + 75000 q^{25} + 25896 q^{28} + 122496 q^{31} + 74724 q^{34} - 56880 q^{40} - 74088 q^{46} + 197448 q^{49} - 149064 q^{52} - 232704 q^{55} - 196140 q^{58} - 1269024 q^{64} - 1585752 q^{70} + 514080 q^{73} + 327984 q^{76} - 1193088 q^{79} + 2813268 q^{82} - 3176832 q^{88} - 68856 q^{94} + 2960832 q^{97} + O(q^{100}) \)

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.h.a 72.h 24.h $24$ $16.564$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

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

\( S_{7}^{\mathrm{old}}(72, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)