Properties

Label 252.2.f
Level 252
Weight 2
Character orbit f
Rep. character \(\chi_{252}(125,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 1
Sturm bound 96
Trace bound 0

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Defining parameters

Level: \( N \) = \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 252.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(252, [\chi])\).

Total New Old
Modular forms 60 4 56
Cusp forms 36 4 32
Eisenstein series 24 0 24

Trace form

\( 4q - 4q^{7} + O(q^{10}) \) \( 4q - 4q^{7} + 28q^{25} - 32q^{37} - 8q^{43} - 20q^{49} + 32q^{67} - 16q^{79} + 48q^{85} - 48q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
252.2.f.a \(4\) \(2.012\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{3}q^{5}+(-1-\beta _{1})q^{7}-\beta _{2}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ \( ( 1 - 2 T^{2} + 25 T^{4} )^{2} \)
$7$ \( ( 1 + 2 T + 7 T^{2} )^{2} \)
$11$ \( ( 1 - 4 T^{2} + 121 T^{4} )^{2} \)
$13$ \( ( 1 - 2 T^{2} + 169 T^{4} )^{2} \)
$17$ \( ( 1 + 22 T^{2} + 289 T^{4} )^{2} \)
$19$ \( ( 1 - 14 T^{2} + 361 T^{4} )^{2} \)
$23$ \( ( 1 - 28 T^{2} + 529 T^{4} )^{2} \)
$29$ \( ( 1 - 40 T^{2} + 841 T^{4} )^{2} \)
$31$ \( ( 1 - 31 T^{2} )^{4} \)
$37$ \( ( 1 + 8 T + 37 T^{2} )^{4} \)
$41$ \( ( 1 + 70 T^{2} + 1681 T^{4} )^{2} \)
$43$ \( ( 1 + 2 T + 43 T^{2} )^{4} \)
$47$ \( ( 1 + 46 T^{2} + 2209 T^{4} )^{2} \)
$53$ \( ( 1 + 56 T^{2} + 2809 T^{4} )^{2} \)
$59$ \( ( 1 - 74 T^{2} + 3481 T^{4} )^{2} \)
$61$ \( ( 1 - 26 T^{2} + 3721 T^{4} )^{2} \)
$67$ \( ( 1 - 8 T + 67 T^{2} )^{4} \)
$71$ \( ( 1 - 124 T^{2} + 5041 T^{4} )^{2} \)
$73$ \( ( 1 - 122 T^{2} + 5329 T^{4} )^{2} \)
$79$ \( ( 1 + 4 T + 79 T^{2} )^{4} \)
$83$ \( ( 1 + 118 T^{2} + 6889 T^{4} )^{2} \)
$89$ \( ( 1 + 70 T^{2} + 7921 T^{4} )^{2} \)
$97$ \( ( 1 - 170 T^{2} + 9409 T^{4} )^{2} \)
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