Properties

Label 28.3.h
Level 28
Weight 3
Character orbit h
Rep. character \(\chi_{28}(5,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 2
Newform subspaces 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 28.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
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 22 2 20
Cusp forms 10 2 8
Eisenstein series 12 0 12

Trace form

\( 2q + 3q^{3} + 3q^{5} - 14q^{7} - 6q^{9} + O(q^{10}) \) \( 2q + 3q^{3} + 3q^{5} - 14q^{7} - 6q^{9} - 15q^{11} + 6q^{15} + 51q^{17} + 27q^{19} - 21q^{21} + 9q^{23} - 22q^{25} - 12q^{29} - 21q^{31} - 45q^{33} - 21q^{35} - 31q^{37} + 24q^{39} + 20q^{43} - 18q^{45} + 75q^{47} + 98q^{49} + 51q^{51} + 57q^{53} + 54q^{57} - 141q^{59} - 141q^{61} + 42q^{63} - 24q^{65} + 49q^{67} - 252q^{71} - 45q^{73} - 66q^{75} + 105q^{77} + 73q^{79} - 9q^{81} + 102q^{85} - 18q^{87} + 99q^{89} - 21q^{93} + 27q^{95} + 180q^{99} + O(q^{100}) \)

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.h.a \(2\) \(0.763\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(3\) \(-14\) \(q+(1+\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}-7q^{7}-6\zeta_{6}q^{9}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(28, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 - 3 T + 12 T^{2} - 27 T^{3} + 81 T^{4} \)
$5$ \( 1 - 3 T + 28 T^{2} - 75 T^{3} + 625 T^{4} \)
$7$ \( ( 1 + 7 T )^{2} \)
$11$ \( 1 + 15 T + 104 T^{2} + 1815 T^{3} + 14641 T^{4} \)
$13$ \( ( 1 - 22 T + 169 T^{2} )( 1 + 22 T + 169 T^{2} ) \)
$17$ \( ( 1 - 17 T )^{2}( 1 - 17 T + 289 T^{2} ) \)
$19$ \( 1 - 27 T + 604 T^{2} - 9747 T^{3} + 130321 T^{4} \)
$23$ \( 1 - 9 T - 448 T^{2} - 4761 T^{3} + 279841 T^{4} \)
$29$ \( ( 1 + 6 T + 841 T^{2} )^{2} \)
$31$ \( 1 + 21 T + 1108 T^{2} + 20181 T^{3} + 923521 T^{4} \)
$37$ \( 1 + 31 T - 408 T^{2} + 42439 T^{3} + 1874161 T^{4} \)
$41$ \( 1 - 290 T^{2} + 2825761 T^{4} \)
$43$ \( ( 1 - 10 T + 1849 T^{2} )^{2} \)
$47$ \( 1 - 75 T + 4084 T^{2} - 165675 T^{3} + 4879681 T^{4} \)
$53$ \( 1 - 57 T + 440 T^{2} - 160113 T^{3} + 7890481 T^{4} \)
$59$ \( 1 + 141 T + 10108 T^{2} + 490821 T^{3} + 12117361 T^{4} \)
$61$ \( 1 + 141 T + 10348 T^{2} + 524661 T^{3} + 13845841 T^{4} \)
$67$ \( 1 - 49 T - 2088 T^{2} - 219961 T^{3} + 20151121 T^{4} \)
$71$ \( ( 1 + 126 T + 5041 T^{2} )^{2} \)
$73$ \( 1 + 45 T + 6004 T^{2} + 239805 T^{3} + 28398241 T^{4} \)
$79$ \( 1 - 73 T - 912 T^{2} - 455593 T^{3} + 38950081 T^{4} \)
$83$ \( 1 - 13586 T^{2} + 47458321 T^{4} \)
$89$ \( 1 - 99 T + 11188 T^{2} - 784179 T^{3} + 62742241 T^{4} \)
$97$ \( 1 - 18050 T^{2} + 88529281 T^{4} \)
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