Properties

Label 15.3.c
Level 15
Weight 3
Character orbit c
Rep. character \(\chi_{15}(11,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 15.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(15, [\chi])\).

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

Trace form

\( 2q - 4q^{3} - 2q^{4} + 10q^{6} - 12q^{7} - 2q^{9} + O(q^{10}) \) \( 2q - 4q^{3} - 2q^{4} + 10q^{6} - 12q^{7} - 2q^{9} + 10q^{10} + 4q^{12} + 32q^{13} - 10q^{15} - 38q^{16} - 40q^{18} - 4q^{19} + 24q^{21} + 20q^{22} + 30q^{24} - 10q^{25} + 44q^{27} + 12q^{28} - 20q^{30} - 36q^{31} - 20q^{33} + 20q^{34} + 2q^{36} - 32q^{37} - 64q^{39} + 30q^{40} - 60q^{42} + 32q^{43} + 40q^{45} + 60q^{46} + 76q^{48} - 26q^{49} - 20q^{51} - 32q^{52} + 70q^{54} - 20q^{55} + 8q^{57} - 140q^{58} + 10q^{60} + 164q^{61} + 12q^{63} - 82q^{64} - 40q^{66} + 48q^{67} - 60q^{69} - 60q^{70} - 120q^{72} - 148q^{73} + 20q^{75} + 4q^{76} + 160q^{78} + 276q^{79} - 158q^{81} + 280q^{82} - 24q^{84} - 20q^{85} + 140q^{87} + 60q^{88} - 10q^{90} - 192q^{91} + 72q^{93} - 220q^{94} - 70q^{96} - 332q^{97} + 80q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(15, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
15.3.c.a \(2\) \(0.409\) \(\Q(\sqrt{-5}) \) None \(0\) \(-4\) \(0\) \(-12\) \(q+\beta q^{2}+(-2-\beta )q^{3}-q^{4}-\beta q^{5}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 - 3 T^{2} + 16 T^{4} \)
$3$ \( 1 + 4 T + 9 T^{2} \)
$5$ \( 1 + 5 T^{2} \)
$7$ \( ( 1 + 6 T + 49 T^{2} )^{2} \)
$11$ \( 1 - 222 T^{2} + 14641 T^{4} \)
$13$ \( ( 1 - 16 T + 169 T^{2} )^{2} \)
$17$ \( 1 - 558 T^{2} + 83521 T^{4} \)
$19$ \( ( 1 + 2 T + 361 T^{2} )^{2} \)
$23$ \( ( 1 - 44 T + 529 T^{2} )( 1 + 44 T + 529 T^{2} ) \)
$29$ \( 1 - 702 T^{2} + 707281 T^{4} \)
$31$ \( ( 1 + 18 T + 961 T^{2} )^{2} \)
$37$ \( ( 1 + 16 T + 1369 T^{2} )^{2} \)
$41$ \( 1 + 558 T^{2} + 2825761 T^{4} \)
$43$ \( ( 1 - 16 T + 1849 T^{2} )^{2} \)
$47$ \( 1 - 1998 T^{2} + 4879681 T^{4} \)
$53$ \( 1 - 5598 T^{2} + 7890481 T^{4} \)
$59$ \( 1 - 6942 T^{2} + 12117361 T^{4} \)
$61$ \( ( 1 - 82 T + 3721 T^{2} )^{2} \)
$67$ \( ( 1 - 24 T + 4489 T^{2} )^{2} \)
$71$ \( 1 + 5598 T^{2} + 25411681 T^{4} \)
$73$ \( ( 1 + 74 T + 5329 T^{2} )^{2} \)
$79$ \( ( 1 - 138 T + 6241 T^{2} )^{2} \)
$83$ \( 1 - 4958 T^{2} + 47458321 T^{4} \)
$89$ \( ( 1 - 142 T + 7921 T^{2} )( 1 + 142 T + 7921 T^{2} ) \)
$97$ \( ( 1 + 166 T + 9409 T^{2} )^{2} \)
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