Properties

Label 29.2.d
Level $29$
Weight $2$
Character orbit 29.d
Rep. character $\chi_{29}(7,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $6$
Newform subspaces $1$
Sturm bound $5$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 29.d (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q(\zeta_{7})\)
Newform subspaces: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(29, [\chi])\).

Total New Old
Modular forms 18 18 0
Cusp forms 6 6 0
Eisenstein series 12 12 0

Trace form

\( 6q - 2q^{2} - 5q^{3} - 2q^{4} + q^{5} - 3q^{6} + q^{7} - 7q^{8} + 6q^{9} + O(q^{10}) \) \( 6q - 2q^{2} - 5q^{3} - 2q^{4} + q^{5} - 3q^{6} + q^{7} - 7q^{8} + 6q^{9} + 9q^{10} - 11q^{11} + 4q^{12} - 5q^{13} + 9q^{14} + 5q^{15} + 4q^{16} + 8q^{17} - 9q^{18} + q^{19} + 2q^{20} + 5q^{21} + 6q^{22} - 7q^{23} + 7q^{24} - 24q^{25} + 4q^{26} - 11q^{27} - 12q^{28} + 6q^{29} - 18q^{30} + 5q^{31} - 13q^{32} + q^{33} + 2q^{34} - q^{35} + 5q^{36} + 11q^{37} + 2q^{38} + 3q^{39} + 14q^{40} + 20q^{41} - 4q^{42} + 13q^{43} + 20q^{44} + q^{45} + 11q^{47} + 6q^{48} - 22q^{49} + q^{50} - 2q^{51} - 10q^{52} + 3q^{53} + 6q^{54} - 17q^{55} - 7q^{56} - 2q^{57} - 16q^{58} - 56q^{59} - 4q^{60} + 3q^{61} + 3q^{62} + 15q^{63} + q^{64} + 5q^{65} - 5q^{66} + 19q^{67} - 12q^{68} - 7q^{69} - 2q^{70} + 21q^{71} - 25q^{73} - 6q^{74} + 48q^{75} - 5q^{76} + 11q^{77} + 13q^{78} - 9q^{79} - 18q^{80} + 18q^{81} - 2q^{82} + 17q^{83} + 3q^{84} - 8q^{85} - 16q^{86} - 5q^{87} + 42q^{88} + 7q^{89} + 2q^{90} + 5q^{91} - 17q^{93} + 8q^{94} + 13q^{95} - 2q^{96} + q^{97} + 19q^{98} - 32q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(29, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
29.2.d.a \(6\) \(0.232\) \(\Q(\zeta_{14})\) None \(-2\) \(-5\) \(1\) \(1\) \(q+(-1+\zeta_{14}+\zeta_{14}^{3}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{2}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + 2 T + 2 T^{2} + 7 T^{3} + 10 T^{4} + 13 T^{5} + 27 T^{6} + 26 T^{7} + 40 T^{8} + 56 T^{9} + 32 T^{10} + 64 T^{11} + 64 T^{12} \)
$3$ \( 1 + 5 T + 8 T^{2} + 4 T^{3} + 3 T^{4} + 3 T^{5} - 8 T^{6} + 9 T^{7} + 27 T^{8} + 108 T^{9} + 648 T^{10} + 1215 T^{11} + 729 T^{12} \)
$5$ \( 1 - T + 10 T^{2} - 12 T^{3} + 81 T^{4} - 91 T^{5} + 456 T^{6} - 455 T^{7} + 2025 T^{8} - 1500 T^{9} + 6250 T^{10} - 3125 T^{11} + 15625 T^{12} \)
$7$ \( 1 - T + 8 T^{2} - 22 T^{3} + 127 T^{4} - 169 T^{5} + 848 T^{6} - 1183 T^{7} + 6223 T^{8} - 7546 T^{9} + 19208 T^{10} - 16807 T^{11} + 117649 T^{12} \)
$11$ \( 1 + 11 T + 68 T^{2} + 354 T^{3} + 1683 T^{4} + 6723 T^{5} + 23296 T^{6} + 73953 T^{7} + 203643 T^{8} + 471174 T^{9} + 995588 T^{10} + 1771561 T^{11} + 1771561 T^{12} \)
$13$ \( 1 + 5 T + 12 T^{2} - 40 T^{3} - 111 T^{4} + 875 T^{5} + 6308 T^{6} + 11375 T^{7} - 18759 T^{8} - 87880 T^{9} + 342732 T^{10} + 1856465 T^{11} + 4826809 T^{12} \)
$17$ \( ( 1 - 4 T + 47 T^{2} - 128 T^{3} + 799 T^{4} - 1156 T^{5} + 4913 T^{6} )^{2} \)
$19$ \( 1 - T - 18 T^{2} + 156 T^{3} + 67 T^{4} - 1127 T^{5} + 9612 T^{6} - 21413 T^{7} + 24187 T^{8} + 1070004 T^{9} - 2345778 T^{10} - 2476099 T^{11} + 47045881 T^{12} \)
$23$ \( 1 + 7 T + 26 T^{2} + 84 T^{3} + 431 T^{4} - 175 T^{5} - 12020 T^{6} - 4025 T^{7} + 227999 T^{8} + 1022028 T^{9} + 7275866 T^{10} + 45054401 T^{11} + 148035889 T^{12} \)
$29$ \( 1 - 6 T - 13 T^{2} + 316 T^{3} - 377 T^{4} - 5046 T^{5} + 24389 T^{6} \)
$31$ \( 1 - 5 T - 34 T^{2} + 388 T^{3} - 1649 T^{4} - 7283 T^{5} + 109220 T^{6} - 225773 T^{7} - 1584689 T^{8} + 11558908 T^{9} - 31399714 T^{10} - 143145755 T^{11} + 887503681 T^{12} \)
$37$ \( 1 - 11 T + 42 T^{2} - 328 T^{3} + 4049 T^{4} - 22869 T^{5} + 100360 T^{6} - 846153 T^{7} + 5543081 T^{8} - 16614184 T^{9} + 78714762 T^{10} - 762783527 T^{11} + 2565726409 T^{12} \)
$41$ \( ( 1 - 10 T + 147 T^{2} - 828 T^{3} + 6027 T^{4} - 16810 T^{5} + 68921 T^{6} )^{2} \)
$43$ \( 1 - 13 T + 42 T^{2} - 50 T^{3} + 251 T^{4} + 17703 T^{5} - 219260 T^{6} + 761229 T^{7} + 464099 T^{8} - 3975350 T^{9} + 143589642 T^{10} - 1911109759 T^{11} + 6321363049 T^{12} \)
$47$ \( 1 - 11 T + 18 T^{2} + 410 T^{3} - 2409 T^{4} - 12679 T^{5} + 224300 T^{6} - 595913 T^{7} - 5321481 T^{8} + 42567430 T^{9} + 87834258 T^{10} - 2522795077 T^{11} + 10779215329 T^{12} \)
$53$ \( 1 - 3 T - 58 T^{2} + 648 T^{3} - 431 T^{4} - 23629 T^{5} + 179088 T^{6} - 1252337 T^{7} - 1210679 T^{8} + 96472296 T^{9} - 457647898 T^{10} - 1254586479 T^{11} + 22164361129 T^{12} \)
$59$ \( ( 1 + 28 T + 429 T^{2} + 4032 T^{3} + 25311 T^{4} + 97468 T^{5} + 205379 T^{6} )^{2} \)
$61$ \( 1 - 3 T - 24 T^{2} - 74 T^{3} + 4633 T^{4} - 24883 T^{5} - 67236 T^{6} - 1517863 T^{7} + 17239393 T^{8} - 16796594 T^{9} - 332300184 T^{10} - 2533788903 T^{11} + 51520374361 T^{12} \)
$67$ \( 1 - 19 T + 168 T^{2} - 904 T^{3} + 1419 T^{4} + 3983 T^{5} + 31592 T^{6} + 266861 T^{7} + 6369891 T^{8} - 271889752 T^{9} + 3385388328 T^{10} - 25652377033 T^{11} + 90458382169 T^{12} \)
$71$ \( 1 - 21 T + 118 T^{2} + 546 T^{3} - 4409 T^{4} - 107373 T^{5} + 1690660 T^{6} - 7623483 T^{7} - 22225769 T^{8} + 195419406 T^{9} + 2998578358 T^{10} - 37888816371 T^{11} + 128100283921 T^{12} \)
$73$ \( 1 + 25 T + 300 T^{2} + 3400 T^{3} + 39069 T^{4} + 348943 T^{5} + 2806700 T^{6} + 25472839 T^{7} + 208198701 T^{8} + 1322657800 T^{9} + 8519472300 T^{10} + 51826789825 T^{11} + 151334226289 T^{12} \)
$79$ \( 1 + 9 T + 2 T^{2} + 210 T^{3} - 977 T^{4} - 72339 T^{5} - 812260 T^{6} - 5714781 T^{7} - 6097457 T^{8} + 103538190 T^{9} + 77900162 T^{10} + 27693507591 T^{11} + 243087455521 T^{12} \)
$83$ \( 1 - 17 T + 136 T^{2} - 1776 T^{3} + 27843 T^{4} - 251219 T^{5} + 1969848 T^{6} - 20851177 T^{7} + 191810427 T^{8} - 1015493712 T^{9} + 6454331656 T^{10} - 66963690931 T^{11} + 326940373369 T^{12} \)
$89$ \( 1 - 7 T + 30 T^{2} + 532 T^{3} + 7389 T^{4} - 23261 T^{5} + 663944 T^{6} - 2070229 T^{7} + 58528269 T^{8} + 375043508 T^{9} + 1882267230 T^{10} - 39088416143 T^{11} + 496981290961 T^{12} \)
$97$ \( 1 - T + 114 T^{2} + 382 T^{3} + 20669 T^{4} + 10611 T^{5} + 2196928 T^{6} + 1029267 T^{7} + 194474621 T^{8} + 348641086 T^{9} + 10092338034 T^{10} - 8587340257 T^{11} + 832972004929 T^{12} \)
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