Properties

Label 15.5.c
Level 15
Weight 5
Character orbit c
Rep. character \(\chi_{15}(11,\cdot)\)
Character field \(\Q\)
Dimension 6
Newform subspaces 1
Sturm bound 10
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 5 \)
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: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(15, [\chi])\).

Total New Old
Modular forms 10 6 4
Cusp forms 6 6 0
Eisenstein series 4 0 4

Trace form

\( 6q + 8q^{3} - 50q^{4} - 2q^{6} + 76q^{7} + 118q^{9} + O(q^{10}) \) \( 6q + 8q^{3} - 50q^{4} - 2q^{6} + 76q^{7} + 118q^{9} + 50q^{10} - 452q^{12} - 424q^{13} + 50q^{15} + 802q^{16} + 1160q^{18} - 244q^{19} - 876q^{21} + 340q^{22} - 786q^{24} - 750q^{25} - 352q^{27} - 3764q^{28} + 2200q^{30} + 3772q^{31} + 4420q^{33} + 3124q^{34} - 7606q^{36} + 1896q^{37} - 1336q^{39} - 4650q^{40} - 1980q^{42} - 7384q^{43} + 1900q^{45} + 8196q^{46} + 14668q^{48} - 1318q^{49} - 8492q^{51} + 8976q^{52} - 278q^{54} - 1300q^{55} - 11584q^{57} - 23740q^{58} + 5050q^{60} + 6452q^{61} + 14796q^{63} + 3174q^{64} - 12760q^{66} + 13816q^{67} + 5472q^{69} - 2100q^{70} - 2040q^{72} + 596q^{73} - 1000q^{75} + 21348q^{76} - 1400q^{78} - 16124q^{79} + 5086q^{81} - 31240q^{82} - 14736q^{84} - 3100q^{85} - 4900q^{87} + 15660q^{88} + 7550q^{90} - 11632q^{91} - 8184q^{93} + 34924q^{94} + 14354q^{96} + 9756q^{97} + 9680q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(15, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
15.5.c.a \(6\) \(1.551\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(8\) \(0\) \(76\) \(q+\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(-8+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 23 T^{2} + 264 T^{4} - 4684 T^{6} + 67584 T^{8} - 1507328 T^{10} + 16777216 T^{12} \)
$3$ \( 1 - 8 T - 27 T^{2} + 504 T^{3} - 2187 T^{4} - 52488 T^{5} + 531441 T^{6} \)
$5$ \( ( 1 + 125 T^{2} )^{3} \)
$7$ \( ( 1 - 38 T + 4653 T^{2} - 114976 T^{3} + 11171853 T^{4} - 219062438 T^{5} + 13841287201 T^{6} )^{2} \)
$11$ \( 1 - 34466 T^{2} + 627812895 T^{4} - 9331838759740 T^{6} + 134577269649570495 T^{8} - \)\(15\!\cdots\!26\)\( T^{10} + \)\(98\!\cdots\!41\)\( T^{12} \)
$13$ \( ( 1 + 212 T + 97943 T^{2} + 12289064 T^{3} + 2797350023 T^{4} + 172934912852 T^{5} + 23298085122481 T^{6} )^{2} \)
$17$ \( 1 - 256778 T^{2} + 40830133839 T^{4} - 4057376310317644 T^{6} + \)\(28\!\cdots\!99\)\( T^{8} - \)\(12\!\cdots\!18\)\( T^{10} + \)\(33\!\cdots\!21\)\( T^{12} \)
$19$ \( ( 1 + 122 T + 284939 T^{2} + 25213796 T^{3} + 37133535419 T^{4} + 2071994691002 T^{5} + 2213314919066161 T^{6} )^{2} \)
$23$ \( 1 - 541878 T^{2} - 37441234461 T^{4} + 62508481606281076 T^{6} - \)\(29\!\cdots\!41\)\( T^{8} - \)\(33\!\cdots\!58\)\( T^{10} + \)\(48\!\cdots\!41\)\( T^{12} \)
$29$ \( 1 - 1427666 T^{2} + 445361323935 T^{4} + 117229967968878500 T^{6} + \)\(22\!\cdots\!35\)\( T^{8} - \)\(35\!\cdots\!86\)\( T^{10} + \)\(12\!\cdots\!81\)\( T^{12} \)
$31$ \( ( 1 - 1886 T + 3804195 T^{2} - 3654810940 T^{3} + 3513253970595 T^{4} - 1608552496613726 T^{5} + 787662783788549761 T^{6} )^{2} \)
$37$ \( ( 1 - 948 T + 3630423 T^{2} - 3404430056 T^{3} + 6803997200103 T^{4} - 3329830522317108 T^{5} + 6582952005840035281 T^{6} )^{2} \)
$41$ \( 1 - 9622286 T^{2} + 49511941482495 T^{4} - \)\(17\!\cdots\!40\)\( T^{6} + \)\(39\!\cdots\!95\)\( T^{8} - \)\(61\!\cdots\!26\)\( T^{10} + \)\(50\!\cdots\!61\)\( T^{12} \)
$43$ \( ( 1 + 3692 T + 9012053 T^{2} + 15407946584 T^{3} + 30810415808453 T^{4} + 43152835424902892 T^{5} + 39959630797262576401 T^{6} )^{2} \)
$47$ \( 1 - 19358678 T^{2} + 191449450821219 T^{4} - \)\(11\!\cdots\!24\)\( T^{6} + \)\(45\!\cdots\!59\)\( T^{8} - \)\(10\!\cdots\!38\)\( T^{10} + \)\(13\!\cdots\!81\)\( T^{12} \)
$53$ \( 1 - 31471178 T^{2} + 496434526631919 T^{4} - \)\(48\!\cdots\!24\)\( T^{6} + \)\(30\!\cdots\!59\)\( T^{8} - \)\(12\!\cdots\!38\)\( T^{10} + \)\(24\!\cdots\!81\)\( T^{12} \)
$59$ \( 1 - 20221586 T^{2} + 518070122195295 T^{4} - \)\(58\!\cdots\!40\)\( T^{6} + \)\(76\!\cdots\!95\)\( T^{8} - \)\(43\!\cdots\!26\)\( T^{10} + \)\(31\!\cdots\!61\)\( T^{12} \)
$61$ \( ( 1 - 3226 T + 32346515 T^{2} - 81211143220 T^{3} + 447864703594115 T^{4} - 618447791729228506 T^{5} + \)\(26\!\cdots\!21\)\( T^{6} )^{2} \)
$67$ \( ( 1 - 6908 T + 65136693 T^{2} - 250302748936 T^{3} + 1312577382182853 T^{4} - 2805115516561276028 T^{5} + \)\(81\!\cdots\!61\)\( T^{6} )^{2} \)
$71$ \( 1 - 121682966 T^{2} + 6612859983587535 T^{4} - \)\(21\!\cdots\!00\)\( T^{6} + \)\(42\!\cdots\!35\)\( T^{8} - \)\(50\!\cdots\!86\)\( T^{10} + \)\(26\!\cdots\!81\)\( T^{12} \)
$73$ \( ( 1 - 298 T + 50688863 T^{2} - 79767435436 T^{3} + 1439474547489983 T^{4} - 240325107384436138 T^{5} + \)\(22\!\cdots\!21\)\( T^{6} )^{2} \)
$79$ \( ( 1 + 8062 T + 112728699 T^{2} + 533077126316 T^{3} + 4390791957074619 T^{4} + 12230931225466694782 T^{5} + \)\(59\!\cdots\!41\)\( T^{6} )^{2} \)
$83$ \( 1 - 211578198 T^{2} + 21276155528463939 T^{4} - \)\(12\!\cdots\!04\)\( T^{6} + \)\(47\!\cdots\!99\)\( T^{8} - \)\(10\!\cdots\!38\)\( T^{10} + \)\(11\!\cdots\!21\)\( T^{12} \)
$89$ \( 1 - 255353766 T^{2} + 32750513998015695 T^{4} - \)\(25\!\cdots\!40\)\( T^{6} + \)\(12\!\cdots\!95\)\( T^{8} - \)\(39\!\cdots\!26\)\( T^{10} + \)\(61\!\cdots\!41\)\( T^{12} \)
$97$ \( ( 1 - 4878 T + 170499663 T^{2} - 362588117636 T^{3} + 15094212576132303 T^{4} - 38231001073370815758 T^{5} + \)\(69\!\cdots\!41\)\( T^{6} )^{2} \)
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