Properties

Label 105.3.e
Level $105$
Weight $3$
Character orbit 105.e
Rep. character $\chi_{105}(34,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(105, [\chi])\).

Total New Old
Modular forms 36 16 20
Cusp forms 28 16 12
Eisenstein series 8 0 8

Trace form

\( 16q - 32q^{4} + 48q^{9} + O(q^{10}) \) \( 16q - 32q^{4} + 48q^{9} - 56q^{11} - 84q^{14} + 24q^{15} + 112q^{16} - 12q^{21} + 16q^{25} - 32q^{29} - 72q^{30} - 4q^{35} - 96q^{36} + 72q^{39} + 568q^{44} - 96q^{46} - 152q^{49} - 96q^{50} + 24q^{51} + 444q^{56} - 288q^{60} - 992q^{64} - 296q^{65} + 504q^{70} - 56q^{71} - 48q^{74} + 464q^{79} + 144q^{81} + 228q^{84} + 608q^{85} - 456q^{86} - 88q^{91} - 24q^{95} - 168q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(105, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
105.3.e.a \(16\) \(2.861\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+\beta _{2}q^{3}+(-2+\beta _{4})q^{4}+(-\beta _{8}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(105, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( ( 1 - 8 T^{2} + 34 T^{4} - 56 T^{6} + 13 T^{8} - 896 T^{10} + 8704 T^{12} - 32768 T^{14} + 65536 T^{16} )^{2} \)
$3$ \( ( 1 - 3 T^{2} )^{8} \)
$5$ \( 1 - 8 T^{2} + 412 T^{4} + 3208 T^{6} - 304250 T^{8} + 2005000 T^{10} + 160937500 T^{12} - 1953125000 T^{14} + 152587890625 T^{16} \)
$7$ \( 1 + 76 T^{2} + 4372 T^{4} + 256564 T^{6} + 11116630 T^{8} + 616010164 T^{10} + 25203709972 T^{12} + 1051937827276 T^{14} + 33232930569601 T^{16} \)
$11$ \( ( 1 + 14 T + 412 T^{2} + 4298 T^{3} + 73702 T^{4} + 520058 T^{5} + 6032092 T^{6} + 24801854 T^{7} + 214358881 T^{8} )^{4} \)
$13$ \( ( 1 + 796 T^{2} + 331060 T^{4} + 90926116 T^{6} + 17935751638 T^{8} + 2596940799076 T^{10} + 270055812494260 T^{12} + 18545275757494876 T^{14} + 665416609183179841 T^{16} )^{2} \)
$17$ \( ( 1 + 844 T^{2} + 436948 T^{4} + 156276148 T^{6} + 48382687318 T^{8} + 13052340157108 T^{10} + 3048043262330068 T^{12} + 491733168221918284 T^{14} + 48661191875666868481 T^{16} )^{2} \)
$19$ \( ( 1 - 2492 T^{2} + 2811124 T^{4} - 1889002244 T^{6} + 831672508246 T^{8} - 246176661440324 T^{10} + 47742901670068084 T^{12} - 5515580778312873212 T^{14} + \)\(28\!\cdots\!81\)\( T^{16} )^{2} \)
$23$ \( ( 1 - 1328 T^{2} + 849580 T^{4} - 574305488 T^{6} + 369064865830 T^{8} - 160714222067408 T^{10} + 66531446875031980 T^{12} - 29102621245722986288 T^{14} + \)\(61\!\cdots\!61\)\( T^{16} )^{2} \)
$29$ \( ( 1 + 8 T + 2080 T^{2} + 33800 T^{3} + 2057614 T^{4} + 28425800 T^{5} + 1471144480 T^{6} + 4758586568 T^{7} + 500246412961 T^{8} )^{4} \)
$31$ \( ( 1 - 3848 T^{2} + 7120156 T^{4} - 9317031800 T^{6} + 9882447105478 T^{8} - 8604474524967800 T^{10} + 6072717237581760796 T^{12} - \)\(30\!\cdots\!28\)\( T^{14} + \)\(72\!\cdots\!81\)\( T^{16} )^{2} \)
$37$ \( ( 1 - 3896 T^{2} + 10011916 T^{4} - 17293616840 T^{6} + 26286367464358 T^{8} - 32411022230471240 T^{10} + 35166649244382922636 T^{12} - \)\(25\!\cdots\!76\)\( T^{14} + \)\(12\!\cdots\!41\)\( T^{16} )^{2} \)
$41$ \( ( 1 - 3764 T^{2} + 15157636 T^{4} - 32470435532 T^{6} + 69381130414198 T^{8} - 91753690379339852 T^{10} + \)\(12\!\cdots\!56\)\( T^{12} - \)\(84\!\cdots\!84\)\( T^{14} + \)\(63\!\cdots\!41\)\( T^{16} )^{2} \)
$43$ \( ( 1 - 12284 T^{2} + 69244228 T^{4} - 235234411460 T^{6} + 528359315216950 T^{8} - 804219641133859460 T^{10} + \)\(80\!\cdots\!28\)\( T^{12} - \)\(49\!\cdots\!84\)\( T^{14} + \)\(13\!\cdots\!01\)\( T^{16} )^{2} \)
$47$ \( ( 1 + 12796 T^{2} + 80087860 T^{4} + 312929425156 T^{6} + 830307264656278 T^{8} + 1526995770274655236 T^{10} + \)\(19\!\cdots\!60\)\( T^{12} + \)\(14\!\cdots\!36\)\( T^{14} + \)\(56\!\cdots\!21\)\( T^{16} )^{2} \)
$53$ \( ( 1 - 8000 T^{2} + 42104908 T^{4} - 150562728128 T^{6} + 466968259413286 T^{8} - 1188012345602149568 T^{10} + \)\(26\!\cdots\!88\)\( T^{12} - \)\(39\!\cdots\!00\)\( T^{14} + \)\(38\!\cdots\!21\)\( T^{16} )^{2} \)
$59$ \( ( 1 - 18308 T^{2} + 161406340 T^{4} - 913248530108 T^{6} + 3699369624469174 T^{8} - 11066162122038004988 T^{10} + \)\(23\!\cdots\!40\)\( T^{12} - \)\(32\!\cdots\!48\)\( T^{14} + \)\(21\!\cdots\!41\)\( T^{16} )^{2} \)
$61$ \( ( 1 - 16940 T^{2} + 152924212 T^{4} - 922409219732 T^{6} + 4001805292894678 T^{8} - 12771531393343334612 T^{10} + \)\(29\!\cdots\!72\)\( T^{12} - \)\(44\!\cdots\!40\)\( T^{14} + \)\(36\!\cdots\!61\)\( T^{16} )^{2} \)
$67$ \( ( 1 - 4700 T^{2} + 31619524 T^{4} - 158634829796 T^{6} + 862906917090742 T^{8} - 3196669650033601316 T^{10} + \)\(12\!\cdots\!84\)\( T^{12} - \)\(38\!\cdots\!00\)\( T^{14} + \)\(16\!\cdots\!81\)\( T^{16} )^{2} \)
$71$ \( ( 1 + 14 T + 11212 T^{2} + 560234 T^{3} + 58945990 T^{4} + 2824139594 T^{5} + 284915767372 T^{6} + 1793403974894 T^{7} + 645753531245761 T^{8} )^{4} \)
$73$ \( ( 1 + 29272 T^{2} + 428373724 T^{4} + 3969975503272 T^{6} + 25265454267874246 T^{8} + \)\(11\!\cdots\!52\)\( T^{10} + \)\(34\!\cdots\!44\)\( T^{12} + \)\(67\!\cdots\!12\)\( T^{14} + \)\(65\!\cdots\!61\)\( T^{16} )^{2} \)
$79$ \( ( 1 - 116 T + 15892 T^{2} - 1623308 T^{3} + 149086294 T^{4} - 10131065228 T^{5} + 618994687252 T^{6} - 28198144840436 T^{7} + 1517108809906561 T^{8} )^{4} \)
$83$ \( ( 1 - 824 T^{2} + 2185948 T^{4} + 170361875704 T^{6} - 285114310603514 T^{8} + 8085088583322532984 T^{10} + \)\(49\!\cdots\!68\)\( T^{12} - \)\(88\!\cdots\!64\)\( T^{14} + \)\(50\!\cdots\!81\)\( T^{16} )^{2} \)
$89$ \( ( 1 - 45764 T^{2} + 1024809508 T^{4} - 14337857169596 T^{6} + 136319750978901046 T^{8} - \)\(89\!\cdots\!36\)\( T^{10} + \)\(40\!\cdots\!48\)\( T^{12} - \)\(11\!\cdots\!44\)\( T^{14} + \)\(15\!\cdots\!61\)\( T^{16} )^{2} \)
$97$ \( ( 1 + 24808 T^{2} + 234463420 T^{4} + 1188451115032 T^{6} + 6842815259264902 T^{8} + \)\(10\!\cdots\!92\)\( T^{10} + \)\(18\!\cdots\!20\)\( T^{12} + \)\(17\!\cdots\!28\)\( T^{14} + \)\(61\!\cdots\!21\)\( T^{16} )^{2} \)
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