Properties

Label 72.22.f
Level $72$
Weight $22$
Character orbit 72.f
Rep. character $\chi_{72}(35,\cdot)$
Character field $\Q$
Dimension $84$
Newform subspaces $1$
Sturm bound $264$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 72.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(264\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(72, [\chi])\).

Total New Old
Modular forms 256 84 172
Cusp forms 248 84 164
Eisenstein series 8 0 8

Trace form

\( 84 q + 2424084 q^{4} + O(q^{10}) \) \( 84 q + 2424084 q^{4} + 17057181612 q^{10} - 4099708064904 q^{16} + 92015527242864 q^{19} - 236011369239528 q^{22} + 8010864257812500 q^{25} - 3042238700022024 q^{28} + 74414158327329924 q^{34} + 75018327243317184 q^{40} + 707788847336454432 q^{43} - 162639476543943288 q^{46} - 5423745715136249124 q^{49} - 70566629446202808 q^{52} - 14491558288019904108 q^{58} - 28749968749508108064 q^{64} - 13653811098426494352 q^{67} + 140256684870035374392 q^{70} - 71781309378863778384 q^{73} + 376055720386305092400 q^{76} - 368362114062816367548 q^{82} - 592572120184082106720 q^{88} - 522206955652189957200 q^{91} - 528772551789914644488 q^{94} - 1686050813935078492512 q^{97} + O(q^{100}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(72, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
72.22.f.a 72.f 24.f $84$ $201.224$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{22}^{\mathrm{old}}(72, [\chi])\) into lower level spaces

\( S_{22}^{\mathrm{old}}(72, [\chi]) \cong \) \(S_{22}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)