↑

Properties

Label 28.3.b
Level 28
Weight 3
Character orbit b
Rep. character \(\chi_{28}(13,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 12
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 28.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(28, [\chi])\).

Total New Old
Modular forms 11 2 9
Cusp forms 5 2 3
Eisenstein series 6 0 6

Trace form

\( 2q + 10q^{7} - 30q^{9} + O(q^{10}) \) \( 2q + 10q^{7} - 30q^{9} - 12q^{11} + 48q^{15} + 48q^{21} - 60q^{23} + 2q^{25} - 12q^{29} - 48q^{35} + 20q^{37} - 48q^{39} + 20q^{43} + 2q^{49} + 192q^{51} + 180q^{53} - 240q^{57} - 150q^{63} + 48q^{65} - 140q^{67} + 84q^{71} - 60q^{77} + 148q^{79} + 18q^{81} - 192q^{85} + 48q^{91} + 240q^{95} + 180q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(28, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
28.3.b.a \(2\) \(0.763\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(10\) \(q+\beta q^{3}-\beta q^{5}+(5-\beta )q^{7}-15q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(28, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(28, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 + 6 T^{2} + 81 T^{4} \)
$5$ \( 1 - 26 T^{2} + 625 T^{4} \)
$7$ \( 1 - 10 T + 49 T^{2} \)
$11$ \( ( 1 + 6 T + 121 T^{2} )^{2} \)
$13$ \( 1 - 314 T^{2} + 28561 T^{4} \)
$17$ \( 1 - 194 T^{2} + 83521 T^{4} \)
$19$ \( 1 - 122 T^{2} + 130321 T^{4} \)
$23$ \( ( 1 + 30 T + 529 T^{2} )^{2} \)
$29$ \( ( 1 + 6 T + 841 T^{2} )^{2} \)
$31$ \( ( 1 - 31 T )^{2}( 1 + 31 T )^{2} \)
$37$ \( ( 1 - 10 T + 1369 T^{2} )^{2} \)
$41$ \( 1 - 962 T^{2} + 2825761 T^{4} \)
$43$ \( ( 1 - 10 T + 1849 T^{2} )^{2} \)
$47$ \( 1 - 4034 T^{2} + 4879681 T^{4} \)
$53$ \( ( 1 - 90 T + 2809 T^{2} )^{2} \)
$59$ \( 1 - 6362 T^{2} + 12117361 T^{4} \)
$61$ \( 1 - 6842 T^{2} + 13845841 T^{4} \)
$67$ \( ( 1 + 70 T + 4489 T^{2} )^{2} \)
$71$ \( ( 1 - 42 T + 5041 T^{2} )^{2} \)
$73$ \( 1 + 958 T^{2} + 28398241 T^{4} \)
$79$ \( ( 1 - 74 T + 6241 T^{2} )^{2} \)
$83$ \( 1 - 9722 T^{2} + 47458321 T^{4} \)
$89$ \( 1 + 5758 T^{2} + 62742241 T^{4} \)
$97$ \( 1 - 12674 T^{2} + 88529281 T^{4} \)
show more
show less