Properties

Label 15.4.b
Level 15
Weight 4
Character orbit b
Rep. character \(\chi_{15}(4,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 15.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(15, [\chi])\).

Total New Old
Modular forms 8 4 4
Cusp forms 4 4 0
Eisenstein series 4 0 4

Trace form

\( 4q - 18q^{4} + 6q^{5} + 18q^{6} - 36q^{9} + O(q^{10}) \) \( 4q - 18q^{4} + 6q^{5} + 18q^{6} - 36q^{9} + 14q^{10} - 84q^{11} + 228q^{14} + 54q^{15} + 50q^{16} - 112q^{19} - 396q^{20} + 36q^{21} - 306q^{24} + 256q^{25} - 12q^{26} + 636q^{29} + 396q^{30} + 104q^{31} - 716q^{34} - 300q^{35} + 162q^{36} - 468q^{39} + 418q^{40} - 816q^{41} + 1116q^{44} - 54q^{45} + 184q^{46} - 140q^{49} - 696q^{50} + 612q^{51} - 162q^{54} - 864q^{55} + 60q^{56} + 372q^{59} + 126q^{60} + 680q^{61} + 958q^{64} + 948q^{65} - 1116q^{66} + 288q^{69} + 1080q^{70} - 72q^{71} - 3132q^{74} - 576q^{75} - 2448q^{76} - 760q^{79} + 444q^{80} + 324q^{81} + 2052q^{84} - 508q^{85} + 4296q^{86} - 2232q^{89} - 126q^{90} + 1944q^{91} + 3232q^{94} + 2784q^{95} - 1854q^{96} + 756q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(15, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
15.4.b.a \(4\) \(0.885\) \(\Q(i, \sqrt{41})\) None \(0\) \(0\) \(6\) \(0\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(-5+\beta _{3})q^{4}+(2+\cdots)q^{5}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 7 T^{2} + 48 T^{4} - 448 T^{6} + 4096 T^{8} \)
$3$ \( ( 1 + 9 T^{2} )^{2} \)
$5$ \( 1 - 6 T - 110 T^{2} - 750 T^{3} + 15625 T^{4} \)
$7$ \( 1 - 616 T^{2} + 316878 T^{4} - 72471784 T^{6} + 13841287201 T^{8} \)
$11$ \( ( 1 + 42 T + 2734 T^{2} + 55902 T^{3} + 1771561 T^{4} )^{2} \)
$13$ \( 1 - 5008 T^{2} + 13678638 T^{4} - 24172659472 T^{6} + 23298085122481 T^{8} \)
$17$ \( 1 - 12400 T^{2} + 76051038 T^{4} - 299305855600 T^{6} + 582622237229761 T^{8} \)
$19$ \( ( 1 + 56 T + 8598 T^{2} + 384104 T^{3} + 47045881 T^{4} )^{2} \)
$23$ \( 1 - 46204 T^{2} + 828262758 T^{4} - 6839850215356 T^{6} + 21914624432020321 T^{8} \)
$29$ \( ( 1 - 318 T + 55978 T^{2} - 7755702 T^{3} + 594823321 T^{4} )^{2} \)
$31$ \( ( 1 - 52 T + 58782 T^{2} - 1549132 T^{3} + 887503681 T^{4} )^{2} \)
$37$ \( 1 - 96016 T^{2} + 4637534478 T^{4} - 246350786886544 T^{6} + 6582952005840035281 T^{8} \)
$41$ \( ( 1 + 408 T + 177982 T^{2} + 28119768 T^{3} + 4750104241 T^{4} )^{2} \)
$43$ \( 1 - 121900 T^{2} + 14997346998 T^{4} - 770574155673100 T^{6} + 39959630797262576401 T^{8} \)
$47$ \( 1 - 225580 T^{2} + 31469120358 T^{4} - 2431575393915820 T^{6} + \)\(11\!\cdots\!41\)\( T^{8} \)
$53$ \( 1 - 376864 T^{2} + 68697431598 T^{4} - 8352949792519456 T^{6} + \)\(49\!\cdots\!41\)\( T^{8} \)
$59$ \( ( 1 - 186 T + 419038 T^{2} - 38200494 T^{3} + 42180533641 T^{4} )^{2} \)
$61$ \( ( 1 - 340 T + 388398 T^{2} - 77173540 T^{3} + 51520374361 T^{4} )^{2} \)
$67$ \( 1 - 861340 T^{2} + 346621507638 T^{4} - 77915422897446460 T^{6} + \)\(81\!\cdots\!61\)\( T^{8} \)
$71$ \( ( 1 + 36 T + 384046 T^{2} + 12884796 T^{3} + 128100283921 T^{4} )^{2} \)
$73$ \( 1 - 429844 T^{2} + 136740794118 T^{4} - 65050109164968916 T^{6} + \)\(22\!\cdots\!21\)\( T^{8} \)
$79$ \( ( 1 + 380 T + 99678 T^{2} + 187354820 T^{3} + 243087455521 T^{4} )^{2} \)
$83$ \( 1 - 916108 T^{2} + 434315280918 T^{4} - 299512691566327852 T^{6} + \)\(10\!\cdots\!61\)\( T^{8} \)
$89$ \( ( 1 + 1116 T + 1508758 T^{2} + 786745404 T^{3} + 496981290961 T^{4} )^{2} \)
$97$ \( 1 - 2174980 T^{2} + 2500346420358 T^{4} - 1811697451280476420 T^{6} + \)\(69\!\cdots\!41\)\( T^{8} \)
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