Properties

Label 43.2.c
Level 43
Weight 2
Character orbit c
Rep. character \(\chi_{43}(6,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 6
Newform subspaces 2
Sturm bound 7
Trace bound 1

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Defining parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 43.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(7\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(43, [\chi])\).

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

Trace form

\( 6q - 4q^{2} + 2q^{3} + 4q^{4} + 3q^{5} - 3q^{6} + q^{7} - 18q^{8} + q^{9} + O(q^{10}) \) \( 6q - 4q^{2} + 2q^{3} + 4q^{4} + 3q^{5} - 3q^{6} + q^{7} - 18q^{8} + q^{9} - 7q^{10} - 10q^{11} - 2q^{12} - 4q^{14} + 3q^{15} + 24q^{16} - 4q^{17} - 4q^{18} - 3q^{19} + 17q^{20} + 28q^{21} + 10q^{22} - 4q^{23} + 4q^{24} + 2q^{25} + 15q^{26} - 10q^{27} - 6q^{28} - 9q^{29} + 3q^{30} - 5q^{31} - 20q^{32} - 10q^{33} - 14q^{34} - 18q^{35} + 19q^{36} + 12q^{37} + 7q^{38} - 20q^{39} - 29q^{40} - 2q^{42} - 34q^{43} + 32q^{45} + 26q^{46} + 2q^{47} + 13q^{48} - 6q^{49} + 17q^{50} - 22q^{51} - 20q^{52} + 10q^{53} - 20q^{54} + 17q^{56} - 3q^{57} + 6q^{58} + 22q^{59} - 13q^{60} + 14q^{61} - 5q^{62} + 23q^{63} + 22q^{64} - 10q^{65} + 5q^{66} + 4q^{67} + 39q^{68} + 21q^{69} + 2q^{70} - 2q^{71} - 33q^{72} - 8q^{73} + 12q^{74} + 6q^{75} - 17q^{76} - 15q^{77} + 10q^{79} + 27q^{80} - 3q^{81} - 30q^{82} - 12q^{83} - 48q^{84} + 42q^{85} + 31q^{86} - 12q^{87} + 10q^{88} - 2q^{89} - 48q^{90} + 20q^{91} - 31q^{92} - 5q^{93} - 58q^{94} + 13q^{95} - 20q^{96} - 32q^{97} - 16q^{98} + 10q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(43, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
43.2.c.a \(2\) \(0.343\) \(\Q(\sqrt{-3}) \) None \(2\) \(-1\) \(1\) \(-3\) \(q+q^{2}+(-1+\zeta_{6})q^{3}-q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
43.2.c.b \(4\) \(0.343\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-6\) \(3\) \(2\) \(4\) \(q+(-2-\beta _{2})q^{2}+(1+\beta _{1}+\beta _{3})q^{3}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 - T + 2 T^{2} )^{2} \))(\( ( 1 + 3 T + 5 T^{2} + 6 T^{3} + 4 T^{4} )^{2} \))
$3$ (\( 1 + T - 2 T^{2} + 3 T^{3} + 9 T^{4} \))(\( 1 - 3 T + 2 T^{2} - 3 T^{3} + 13 T^{4} - 9 T^{5} + 18 T^{6} - 81 T^{7} + 81 T^{8} \))
$5$ (\( 1 - T - 4 T^{2} - 5 T^{3} + 25 T^{4} \))(\( 1 - 2 T - 2 T^{2} + 8 T^{3} - 9 T^{4} + 40 T^{5} - 50 T^{6} - 250 T^{7} + 625 T^{8} \))
$7$ (\( 1 + 3 T + 2 T^{2} + 21 T^{3} + 49 T^{4} \))(\( 1 - 4 T + 3 T^{2} + 4 T^{3} + 8 T^{4} + 28 T^{5} + 147 T^{6} - 1372 T^{7} + 2401 T^{8} \))
$11$ (\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 + 5 T + 27 T^{2} + 55 T^{3} + 121 T^{4} )^{2} \))
$13$ (\( ( 1 - 7 T + 13 T^{2} )( 1 + 2 T + 13 T^{2} ) \))(\( 1 + 5 T - 6 T^{2} + 25 T^{3} + 467 T^{4} + 325 T^{5} - 1014 T^{6} + 10985 T^{7} + 28561 T^{8} \))
$17$ (\( 1 + 3 T - 8 T^{2} + 51 T^{3} + 289 T^{4} \))(\( 1 + T - 2 T^{2} - 31 T^{3} - 297 T^{4} - 527 T^{5} - 578 T^{6} + 4913 T^{7} + 83521 T^{8} \))
$19$ (\( ( 1 - 7 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \))(\( 1 + 2 T - 30 T^{2} - 8 T^{3} + 719 T^{4} - 152 T^{5} - 10830 T^{6} + 13718 T^{7} + 130321 T^{8} \))
$23$ (\( 1 - 7 T + 26 T^{2} - 161 T^{3} + 529 T^{4} \))(\( 1 + 11 T + 46 T^{2} + 319 T^{3} + 2313 T^{4} + 7337 T^{5} + 24334 T^{6} + 133837 T^{7} + 279841 T^{8} \))
$29$ (\( 1 + 3 T - 20 T^{2} + 87 T^{3} + 841 T^{4} \))(\( ( 1 + 3 T - 20 T^{2} + 87 T^{3} + 841 T^{4} )^{2} \))
$31$ (\( 1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4} \))(\( ( 1 - 31 T^{2} + 961 T^{4} )^{2} \))
$37$ (\( 1 - 9 T + 44 T^{2} - 333 T^{3} + 1369 T^{4} \))(\( 1 - 3 T - 56 T^{2} + 27 T^{3} + 2523 T^{4} + 999 T^{5} - 76664 T^{6} - 151959 T^{7} + 1874161 T^{8} \))
$41$ (\( ( 1 + 10 T + 41 T^{2} )^{2} \))(\( ( 1 - 10 T + 87 T^{2} - 410 T^{3} + 1681 T^{4} )^{2} \))
$43$ (\( 1 + 8 T + 43 T^{2} \))(\( ( 1 + 13 T + 43 T^{2} )^{2} \))
$47$ (\( ( 1 + 8 T + 47 T^{2} )^{2} \))(\( ( 1 - 9 T + 103 T^{2} - 423 T^{3} + 2209 T^{4} )^{2} \))
$53$ (\( 1 - 5 T - 28 T^{2} - 265 T^{3} + 2809 T^{4} \))(\( 1 - 5 T - 86 T^{2} - 25 T^{3} + 8187 T^{4} - 1325 T^{5} - 241574 T^{6} - 744385 T^{7} + 7890481 T^{8} \))
$59$ (\( ( 1 - 12 T + 59 T^{2} )^{2} \))(\( ( 1 + T + 87 T^{2} + 59 T^{3} + 3481 T^{4} )^{2} \))
$61$ (\( ( 1 - 14 T + 61 T^{2} )( 1 + T + 61 T^{2} ) \))(\( 1 - T - 110 T^{2} + 11 T^{3} + 8539 T^{4} + 671 T^{5} - 409310 T^{6} - 226981 T^{7} + 13845841 T^{8} \))
$67$ (\( 1 - 3 T - 58 T^{2} - 201 T^{3} + 4489 T^{4} \))(\( 1 - T - 122 T^{2} + 11 T^{3} + 10573 T^{4} + 737 T^{5} - 547658 T^{6} - 300763 T^{7} + 20151121 T^{8} \))
$71$ (\( 1 - T - 70 T^{2} - 71 T^{3} + 5041 T^{4} \))(\( 1 + 3 T + 16 T^{2} - 447 T^{3} - 5631 T^{4} - 31737 T^{5} + 80656 T^{6} + 1073733 T^{7} + 25411681 T^{8} \))
$73$ (\( 1 + 11 T + 48 T^{2} + 803 T^{3} + 5329 T^{4} \))(\( 1 - 3 T - 128 T^{2} + 27 T^{3} + 12783 T^{4} + 1971 T^{5} - 682112 T^{6} - 1167051 T^{7} + 28398241 T^{8} \))
$79$ (\( 1 - 5 T - 54 T^{2} - 395 T^{3} + 6241 T^{4} \))(\( 1 - 5 T - 138 T^{2} - 25 T^{3} + 18353 T^{4} - 1975 T^{5} - 861258 T^{6} - 2465195 T^{7} + 38950081 T^{8} \))
$83$ (\( 1 + 9 T - 2 T^{2} + 747 T^{3} + 6889 T^{4} \))(\( 1 + 3 T + 52 T^{2} - 627 T^{3} - 5787 T^{4} - 52041 T^{5} + 358228 T^{6} + 1715361 T^{7} + 47458321 T^{8} \))
$89$ (\( 1 - T - 88 T^{2} - 89 T^{3} + 7921 T^{4} \))(\( 1 + 3 T - 160 T^{2} - 27 T^{3} + 19839 T^{4} - 2403 T^{5} - 1267360 T^{6} + 2114907 T^{7} + 62742241 T^{8} \))
$97$ (\( ( 1 + 2 T + 97 T^{2} )^{2} \))(\( ( 1 + 14 T + 238 T^{2} + 1358 T^{3} + 9409 T^{4} )^{2} \))
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