Properties

Label 28.2.d
Level 28
Weight 2
Character orbit d
Rep. character \(\chi_{28}(27,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 28.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 28 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(28, [\chi])\).

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

Trace form

\( 2q - q^{2} - 3q^{4} + 5q^{8} - 6q^{9} + O(q^{10}) \) \( 2q - q^{2} - 3q^{4} + 5q^{8} - 6q^{9} + 7q^{14} + q^{16} + 3q^{18} - 14q^{22} + 10q^{25} - 7q^{28} - 4q^{29} - 11q^{32} + 9q^{36} + 12q^{37} + 14q^{44} + 14q^{46} - 14q^{49} - 5q^{50} - 20q^{53} - 7q^{56} + 2q^{58} + 9q^{64} - 15q^{72} - 6q^{74} + 28q^{77} + 18q^{81} - 14q^{86} + 14q^{88} - 14q^{92} + 7q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(28, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
28.2.d.a \(2\) \(0.224\) \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) \(-1\) \(0\) \(0\) \(0\) \(q-\beta q^{2}+(-2+\beta )q^{4}+(-1+2\beta )q^{7}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + T + 2 T^{2} \)
$3$ \( ( 1 + 3 T^{2} )^{2} \)
$5$ \( ( 1 - 5 T^{2} )^{2} \)
$7$ \( 1 + 7 T^{2} \)
$11$ \( ( 1 - 4 T + 11 T^{2} )( 1 + 4 T + 11 T^{2} ) \)
$13$ \( ( 1 - 13 T^{2} )^{2} \)
$17$ \( ( 1 - 17 T^{2} )^{2} \)
$19$ \( ( 1 + 19 T^{2} )^{2} \)
$23$ \( ( 1 - 8 T + 23 T^{2} )( 1 + 8 T + 23 T^{2} ) \)
$29$ \( ( 1 + 2 T + 29 T^{2} )^{2} \)
$31$ \( ( 1 + 31 T^{2} )^{2} \)
$37$ \( ( 1 - 6 T + 37 T^{2} )^{2} \)
$41$ \( ( 1 - 41 T^{2} )^{2} \)
$43$ \( ( 1 - 12 T + 43 T^{2} )( 1 + 12 T + 43 T^{2} ) \)
$47$ \( ( 1 + 47 T^{2} )^{2} \)
$53$ \( ( 1 + 10 T + 53 T^{2} )^{2} \)
$59$ \( ( 1 + 59 T^{2} )^{2} \)
$61$ \( ( 1 - 61 T^{2} )^{2} \)
$67$ \( ( 1 - 4 T + 67 T^{2} )( 1 + 4 T + 67 T^{2} ) \)
$71$ \( ( 1 - 16 T + 71 T^{2} )( 1 + 16 T + 71 T^{2} ) \)
$73$ \( ( 1 - 73 T^{2} )^{2} \)
$79$ \( ( 1 - 8 T + 79 T^{2} )( 1 + 8 T + 79 T^{2} ) \)
$83$ \( ( 1 + 83 T^{2} )^{2} \)
$89$ \( ( 1 - 89 T^{2} )^{2} \)
$97$ \( ( 1 - 97 T^{2} )^{2} \)
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