Properties

Label 72.2.f
Level 72
Weight 2
Character orbit f
Rep. character \(\chi_{72}(35,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 1
Sturm bound 24
Trace bound 0

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Defining parameters

Level: \( N \) = \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) = \( 2 \)
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: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(72, [\chi])\).

Total New Old
Modular forms 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

Trace form

\( 4q + 4q^{4} + O(q^{10}) \) \( 4q + 4q^{4} - 12q^{10} - 8q^{16} - 16q^{19} + 8q^{22} + 4q^{25} + 24q^{28} - 4q^{34} + 32q^{43} + 24q^{46} - 20q^{49} - 24q^{52} + 12q^{58} - 32q^{64} - 16q^{67} - 24q^{70} - 16q^{73} - 16q^{76} - 4q^{82} + 32q^{88} + 48q^{91} - 24q^{94} + 32q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(72, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
72.2.f.a \(4\) \(0.575\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{4}+(-2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(72, [\chi])\) into lower level spaces

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

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 - 2 T^{2} + 4 T^{4} \)
$3$ 1
$5$ \( ( 1 + 4 T^{2} + 25 T^{4} )^{2} \)
$7$ \( ( 1 - 4 T + 7 T^{2} )^{2}( 1 + 4 T + 7 T^{2} )^{2} \)
$11$ \( ( 1 - 6 T + 11 T^{2} )^{2}( 1 + 6 T + 11 T^{2} )^{2} \)
$13$ \( ( 1 - 14 T^{2} + 169 T^{4} )^{2} \)
$17$ \( ( 1 - 32 T^{2} + 289 T^{4} )^{2} \)
$19$ \( ( 1 + 4 T + 19 T^{2} )^{4} \)
$23$ \( ( 1 + 22 T^{2} + 529 T^{4} )^{2} \)
$29$ \( ( 1 + 52 T^{2} + 841 T^{4} )^{2} \)
$31$ \( ( 1 - 50 T^{2} + 961 T^{4} )^{2} \)
$37$ \( ( 1 - 37 T^{2} )^{4} \)
$41$ \( ( 1 - 80 T^{2} + 1681 T^{4} )^{2} \)
$43$ \( ( 1 - 8 T + 43 T^{2} )^{4} \)
$47$ \( ( 1 + 70 T^{2} + 2209 T^{4} )^{2} \)
$53$ \( ( 1 + 52 T^{2} + 2809 T^{4} )^{2} \)
$59$ \( ( 1 + 10 T^{2} + 3481 T^{4} )^{2} \)
$61$ \( ( 1 + 70 T^{2} + 3721 T^{4} )^{2} \)
$67$ \( ( 1 + 4 T + 67 T^{2} )^{4} \)
$71$ \( ( 1 - 74 T^{2} + 5041 T^{4} )^{2} \)
$73$ \( ( 1 + 4 T + 73 T^{2} )^{4} \)
$79$ \( ( 1 - 146 T^{2} + 6241 T^{4} )^{2} \)
$83$ \( ( 1 + 34 T^{2} + 6889 T^{4} )^{2} \)
$89$ \( ( 1 - 128 T^{2} + 7921 T^{4} )^{2} \)
$97$ \( ( 1 - 8 T + 97 T^{2} )^{4} \)
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