Properties

Label 5.10.b
Level 5
Weight 10
Character orbit b
Rep. character \(\chi_{5}(4,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 5.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(5, [\chi])\).

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

Trace form

\( 4q - 1368q^{4} + 1140q^{5} + 2808q^{6} + 11628q^{9} + O(q^{10}) \) \( 4q - 1368q^{4} + 1140q^{5} + 2808q^{6} + 11628q^{9} - 69160q^{10} + 109968q^{11} - 424536q^{14} - 396720q^{15} + 1631264q^{16} - 636880q^{19} - 3302280q^{20} + 3523968q^{21} - 2435040q^{24} - 1337900q^{25} + 6618768q^{26} - 3531720q^{29} + 3712680q^{30} - 10587712q^{31} + 26434624q^{34} + 13629840q^{35} - 56399976q^{36} + 1686816q^{39} + 43578400q^{40} - 16788552q^{41} + 20638944q^{44} + 55737180q^{45} - 61250072q^{46} - 46921028q^{49} - 150092400q^{50} + 84017088q^{51} + 115855920q^{54} - 26907120q^{55} + 315178080q^{56} - 460829040q^{59} - 307006560q^{60} + 360490568q^{61} + 134995072q^{64} + 183895680q^{65} + 18949536q^{66} - 286524864q^{69} - 508341960q^{70} - 47611872q^{71} + 1176861744q^{74} + 659239200q^{75} - 1168489440q^{76} - 728043520q^{79} + 965843040q^{80} - 343387836q^{81} + 1118898144q^{84} + 1275419840q^{85} - 2375904552q^{86} - 1582700760q^{89} - 1197088920q^{90} + 473322528q^{91} + 3327101704q^{94} + 1204791600q^{95} + 399339648q^{96} - 728787024q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(5, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
5.10.b.a \(4\) \(2.575\) 4.0.49740556.1 None \(0\) \(0\) \(1140\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-342+\cdots)q^{4}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 - 340 T^{2} - 174912 T^{4} - 89128960 T^{6} + 68719476736 T^{8} \)
$3$ \( 1 - 45180 T^{2} + 1049244678 T^{4} - 17503657693020 T^{6} + 150094635296999121 T^{8} \)
$5$ \( 1 - 1140 T + 1318750 T^{2} - 2226562500 T^{3} + 3814697265625 T^{4} \)
$7$ \( 1 - 57246700 T^{2} + 3508143545353398 T^{4} - \)\(93\!\cdots\!00\)\( T^{6} + \)\(26\!\cdots\!01\)\( T^{8} \)
$11$ \( ( 1 - 54984 T + 5180465446 T^{2} - 129649395841944 T^{3} + 5559917313492231481 T^{4} )^{2} \)
$13$ \( 1 - 35613791860 T^{2} + \)\(53\!\cdots\!58\)\( T^{4} - \)\(40\!\cdots\!40\)\( T^{6} + \)\(12\!\cdots\!41\)\( T^{8} \)
$17$ \( 1 - 285780369220 T^{2} + \)\(48\!\cdots\!18\)\( T^{4} - \)\(40\!\cdots\!80\)\( T^{6} + \)\(19\!\cdots\!81\)\( T^{8} \)
$19$ \( ( 1 + 318440 T + 505756418358 T^{2} + 102756670480744760 T^{3} + \)\(10\!\cdots\!41\)\( T^{4} )^{2} \)
$23$ \( 1 - 5779790962540 T^{2} + \)\(14\!\cdots\!38\)\( T^{4} - \)\(18\!\cdots\!60\)\( T^{6} + \)\(10\!\cdots\!61\)\( T^{8} \)
$29$ \( ( 1 + 1765860 T + 26950935551038 T^{2} + 25617588792948032340 T^{3} + \)\(21\!\cdots\!61\)\( T^{4} )^{2} \)
$31$ \( ( 1 + 5293856 T + 59464921598526 T^{2} + \)\(13\!\cdots\!76\)\( T^{3} + \)\(69\!\cdots\!41\)\( T^{4} )^{2} \)
$37$ \( 1 - 231603274936660 T^{2} + \)\(44\!\cdots\!58\)\( T^{4} - \)\(39\!\cdots\!40\)\( T^{6} + \)\(28\!\cdots\!41\)\( T^{8} \)
$41$ \( ( 1 + 8394276 T + 221313076168966 T^{2} + \)\(27\!\cdots\!36\)\( T^{3} + \)\(10\!\cdots\!21\)\( T^{4} )^{2} \)
$43$ \( 1 - 614109141147100 T^{2} + \)\(57\!\cdots\!98\)\( T^{4} - \)\(15\!\cdots\!00\)\( T^{6} + \)\(63\!\cdots\!01\)\( T^{8} \)
$47$ \( 1 - 1368976020813580 T^{2} + \)\(29\!\cdots\!78\)\( T^{4} - \)\(17\!\cdots\!20\)\( T^{6} + \)\(15\!\cdots\!21\)\( T^{8} \)
$53$ \( 1 - 7684297973864980 T^{2} + \)\(36\!\cdots\!78\)\( T^{4} - \)\(83\!\cdots\!20\)\( T^{6} + \)\(11\!\cdots\!21\)\( T^{8} \)
$59$ \( ( 1 + 230414520 T + 28555631923987078 T^{2} + \)\(19\!\cdots\!80\)\( T^{3} + \)\(75\!\cdots\!21\)\( T^{4} )^{2} \)
$61$ \( ( 1 - 180245284 T + 30154717014478446 T^{2} - \)\(21\!\cdots\!44\)\( T^{3} + \)\(13\!\cdots\!81\)\( T^{4} )^{2} \)
$67$ \( 1 + 41160407446058180 T^{2} + \)\(18\!\cdots\!18\)\( T^{4} + \)\(30\!\cdots\!20\)\( T^{6} + \)\(54\!\cdots\!81\)\( T^{8} \)
$71$ \( ( 1 + 23805936 T + 85782754020107086 T^{2} + \)\(10\!\cdots\!16\)\( T^{3} + \)\(21\!\cdots\!61\)\( T^{4} )^{2} \)
$73$ \( 1 - 229489314868712740 T^{2} + \)\(20\!\cdots\!38\)\( T^{4} - \)\(79\!\cdots\!60\)\( T^{6} + \)\(12\!\cdots\!61\)\( T^{8} \)
$79$ \( ( 1 + 364021760 T + 220545463862625438 T^{2} + \)\(43\!\cdots\!40\)\( T^{3} + \)\(14\!\cdots\!61\)\( T^{4} )^{2} \)
$83$ \( 1 - 434569632367965820 T^{2} + \)\(10\!\cdots\!18\)\( T^{4} - \)\(15\!\cdots\!80\)\( T^{6} + \)\(12\!\cdots\!81\)\( T^{8} \)
$89$ \( ( 1 + 791350380 T + 832192702699668118 T^{2} + \)\(27\!\cdots\!20\)\( T^{3} + \)\(12\!\cdots\!81\)\( T^{4} )^{2} \)
$97$ \( 1 - 2561123777205326980 T^{2} + \)\(27\!\cdots\!78\)\( T^{4} - \)\(14\!\cdots\!20\)\( T^{6} + \)\(33\!\cdots\!21\)\( T^{8} \)
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