Properties

Label 6014.2.a
Level 6014
Weight 2
Character orbit a
Rep. character \(\chi_{6014}(1,\cdot)\)
Character field \(\Q\)
Dimension 239
Newform subspaces 12
Sturm bound 1568
Trace bound 3

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Defining parameters

Level: \( N \) \(=\) \( 6014 = 2 \cdot 31 \cdot 97 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6014.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(1568\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6014))\).

Total New Old
Modular forms 788 239 549
Cusp forms 781 239 542
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(31\)\(97\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(26\)
\(+\)\(+\)\(-\)\(-\)\(34\)
\(+\)\(-\)\(+\)\(-\)\(38\)
\(+\)\(-\)\(-\)\(+\)\(22\)
\(-\)\(+\)\(+\)\(-\)\(33\)
\(-\)\(+\)\(-\)\(+\)\(27\)
\(-\)\(-\)\(+\)\(+\)\(21\)
\(-\)\(-\)\(-\)\(-\)\(38\)
Plus space\(+\)\(96\)
Minus space\(-\)\(143\)

Trace form

\( 239q - q^{2} - 4q^{3} + 239q^{4} + 6q^{5} + 4q^{6} - q^{8} + 235q^{9} + O(q^{10}) \) \( 239q - q^{2} - 4q^{3} + 239q^{4} + 6q^{5} + 4q^{6} - q^{8} + 235q^{9} - 2q^{10} + 4q^{11} - 4q^{12} + 2q^{13} + 16q^{14} + 32q^{15} + 239q^{16} + 22q^{17} + 3q^{18} + 16q^{19} + 6q^{20} + 8q^{21} - 12q^{22} + 8q^{23} + 4q^{24} + 233q^{25} - 6q^{26} + 8q^{27} + 10q^{29} - q^{31} - q^{32} + 32q^{33} - 18q^{34} + 40q^{35} + 235q^{36} - 30q^{37} - 8q^{38} + 64q^{39} - 2q^{40} + 6q^{41} + 24q^{42} + 12q^{43} + 4q^{44} + 94q^{45} + 8q^{46} + 32q^{47} - 4q^{48} + 271q^{49} + 17q^{50} - 48q^{51} + 2q^{52} + 26q^{53} + 16q^{54} + 32q^{55} + 16q^{56} + 16q^{57} - 30q^{58} + 40q^{59} + 32q^{60} - 14q^{61} - q^{62} + 40q^{63} + 239q^{64} - 20q^{65} - 16q^{66} - 32q^{67} + 22q^{68} - 8q^{69} + 8q^{70} - 24q^{71} + 3q^{72} + 30q^{73} - 6q^{74} - 60q^{75} + 16q^{76} - 32q^{77} - 48q^{79} + 6q^{80} + 183q^{81} - 18q^{82} - 4q^{83} + 8q^{84} - 12q^{85} - 20q^{86} - 40q^{87} - 12q^{88} + 6q^{89} - 26q^{90} - 48q^{91} + 8q^{92} - 4q^{93} + 64q^{94} - 32q^{95} + 4q^{96} + 3q^{97} - 33q^{98} - 52q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6014))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 31 97
6014.2.a.a \(1\) \(48.022\) \(\Q\) None \(1\) \(-1\) \(3\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+q^{8}+\cdots\)
6014.2.a.b \(1\) \(48.022\) \(\Q\) None \(1\) \(0\) \(2\) \(-4\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+2q^{5}-4q^{7}+q^{8}-3q^{9}+\cdots\)
6014.2.a.c \(2\) \(48.022\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(4\) \(-4\) \(+\) \(+\) \(-\) \(q-q^{2}+2\beta q^{3}+q^{4}+(2+\beta )q^{5}-2\beta q^{6}+\cdots\)
6014.2.a.d \(5\) \(48.022\) 5.5.380224.1 None \(5\) \(0\) \(-4\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{4})q^{5}+\cdots\)
6014.2.a.e \(21\) \(48.022\) None \(21\) \(-10\) \(-10\) \(-11\) \(-\) \(-\) \(+\)
6014.2.a.f \(22\) \(48.022\) None \(-22\) \(0\) \(0\) \(-11\) \(+\) \(-\) \(-\)
6014.2.a.g \(26\) \(48.022\) None \(-26\) \(0\) \(-2\) \(-1\) \(+\) \(+\) \(+\)
6014.2.a.h \(26\) \(48.022\) None \(26\) \(-10\) \(-8\) \(-9\) \(-\) \(+\) \(-\)
6014.2.a.i \(28\) \(48.022\) None \(28\) \(12\) \(10\) \(13\) \(-\) \(+\) \(+\)
6014.2.a.j \(32\) \(48.022\) None \(-32\) \(-2\) \(0\) \(5\) \(+\) \(+\) \(-\)
6014.2.a.k \(37\) \(48.022\) None \(37\) \(9\) \(9\) \(19\) \(-\) \(-\) \(-\)
6014.2.a.l \(38\) \(48.022\) None \(-38\) \(-2\) \(2\) \(3\) \(+\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6014))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6014)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(97))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(194))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3007))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 - T \))(\( 1 - T \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{5} \))
$3$ (\( 1 + T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 - 2 T^{2} + 9 T^{4} \))(\( 1 + 7 T^{2} - 2 T^{3} + 23 T^{4} - 10 T^{5} + 69 T^{6} - 18 T^{7} + 189 T^{8} + 243 T^{10} \))
$5$ (\( 1 - 3 T + 5 T^{2} \))(\( 1 - 2 T + 5 T^{2} \))(\( 1 - 4 T + 12 T^{2} - 20 T^{3} + 25 T^{4} \))(\( 1 + 4 T + 21 T^{2} + 50 T^{3} + 163 T^{4} + 298 T^{5} + 815 T^{6} + 1250 T^{7} + 2625 T^{8} + 2500 T^{9} + 3125 T^{10} \))
$7$ (\( 1 + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 + 4 T + 16 T^{2} + 28 T^{3} + 49 T^{4} \))(\( ( 1 + 7 T^{2} )^{5} \))
$11$ (\( 1 - T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( ( 1 - 4 T + 11 T^{2} )^{2} \))(\( 1 - 4 T + 47 T^{2} - 154 T^{3} + 959 T^{4} - 2446 T^{5} + 10549 T^{6} - 18634 T^{7} + 62557 T^{8} - 58564 T^{9} + 161051 T^{10} \))
$13$ (\( 1 - 6 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( ( 1 + 13 T^{2} )^{2} \))(\( 1 + 25 T^{2} + 32 T^{3} + 402 T^{4} + 704 T^{5} + 5226 T^{6} + 5408 T^{7} + 54925 T^{8} + 371293 T^{10} \))
$17$ (\( 1 + T + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))(\( 1 + 32 T^{2} + 289 T^{4} \))(\( 1 - 14 T + 139 T^{2} - 904 T^{3} + 4977 T^{4} - 21638 T^{5} + 84609 T^{6} - 261256 T^{7} + 682907 T^{8} - 1169294 T^{9} + 1419857 T^{10} \))
$19$ (\( 1 - 7 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( ( 1 + 6 T + 19 T^{2} )^{2} \))(\( 1 + 10 T + 115 T^{2} + 706 T^{3} + 4539 T^{4} + 19436 T^{5} + 86241 T^{6} + 254866 T^{7} + 788785 T^{8} + 1303210 T^{9} + 2476099 T^{10} \))
$23$ (\( 1 - 7 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 14 T^{2} + 529 T^{4} \))(\( 1 + 25 T^{2} - 12 T^{3} + 921 T^{4} + 116 T^{5} + 21183 T^{6} - 6348 T^{7} + 304175 T^{8} + 6436343 T^{10} \))
$29$ (\( 1 + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 - 8 T + 42 T^{2} - 232 T^{3} + 841 T^{4} \))(\( 1 - 12 T + 129 T^{2} - 688 T^{3} + 4106 T^{4} - 16392 T^{5} + 119074 T^{6} - 578608 T^{7} + 3146181 T^{8} - 8487372 T^{9} + 20511149 T^{10} \))
$31$ (\( 1 - T \))(\( 1 + T \))(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{5} \))
$37$ (\( 1 + 4 T + 37 T^{2} \))(\( 1 + 6 T + 37 T^{2} \))(\( 1 + 8 T + 58 T^{2} + 296 T^{3} + 1369 T^{4} \))(\( ( 1 + 37 T^{2} )^{5} \))
$41$ (\( 1 - 2 T + 41 T^{2} \))(\( 1 - 2 T + 41 T^{2} \))(\( 1 - 12 T + 110 T^{2} - 492 T^{3} + 1681 T^{4} \))(\( 1 - 2 T + 37 T^{2} + 8 T^{3} + 2210 T^{4} + 2036 T^{5} + 90610 T^{6} + 13448 T^{7} + 2550077 T^{8} - 5651522 T^{9} + 115856201 T^{10} \))
$43$ (\( 1 + 11 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 + 14 T^{2} + 1849 T^{4} \))(\( 1 + 4 T + 207 T^{2} + 666 T^{3} + 17471 T^{4} + 42510 T^{5} + 751253 T^{6} + 1231434 T^{7} + 16457949 T^{8} + 13675204 T^{9} + 147008443 T^{10} \))
$47$ (\( 1 + 13 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))(\( ( 1 - 4 T + 47 T^{2} )^{2} \))(\( 1 - 40 T + 797 T^{2} - 10576 T^{3} + 104729 T^{4} - 808656 T^{5} + 4922263 T^{6} - 23362384 T^{7} + 82746931 T^{8} - 195187240 T^{9} + 229345007 T^{10} \))
$53$ (\( 1 + T + 53 T^{2} \))(\( 1 + 14 T + 53 T^{2} \))(\( 1 - 16 T + 162 T^{2} - 848 T^{3} + 2809 T^{4} \))(\( 1 - 30 T + 553 T^{2} - 7170 T^{3} + 72343 T^{4} - 584676 T^{5} + 3834179 T^{6} - 20140530 T^{7} + 82328981 T^{8} - 236714430 T^{9} + 418195493 T^{10} \))
$59$ (\( 1 - 7 T + 59 T^{2} \))(\( 1 + 4 T + 59 T^{2} \))(\( 1 - 20 T + 210 T^{2} - 1180 T^{3} + 3481 T^{4} \))(\( 1 - 22 T + 387 T^{2} - 4530 T^{3} + 46739 T^{4} - 377552 T^{5} + 2757601 T^{6} - 15768930 T^{7} + 79481673 T^{8} - 266581942 T^{9} + 714924299 T^{10} \))
$61$ (\( 1 - 10 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 8 T + 66 T^{2} + 488 T^{3} + 3721 T^{4} \))(\( 1 + 16 T + 361 T^{2} + 3808 T^{3} + 46870 T^{4} + 344992 T^{5} + 2859070 T^{6} + 14169568 T^{7} + 81940141 T^{8} + 221533456 T^{9} + 844596301 T^{10} \))
$67$ (\( 1 + 4 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 - 4 T + 66 T^{2} - 268 T^{3} + 4489 T^{4} \))(\( 1 - 4 T + 167 T^{2} - 880 T^{3} + 18502 T^{4} - 65192 T^{5} + 1239634 T^{6} - 3950320 T^{7} + 50227421 T^{8} - 80604484 T^{9} + 1350125107 T^{10} \))
$71$ (\( 1 - 10 T + 71 T^{2} \))(\( 1 + 12 T + 71 T^{2} \))(\( 1 - 4 T + 128 T^{2} - 284 T^{3} + 5041 T^{4} \))(\( 1 + 40 T + 955 T^{2} + 15552 T^{3} + 191794 T^{4} + 1821488 T^{5} + 13617374 T^{6} + 78397632 T^{7} + 341805005 T^{8} + 1016467240 T^{9} + 1804229351 T^{10} \))
$73$ (\( 1 + 4 T + 73 T^{2} \))(\( 1 - 2 T + 73 T^{2} \))(\( 1 - 4 T + 118 T^{2} - 292 T^{3} + 5329 T^{4} \))(\( 1 - 18 T + 301 T^{2} - 2216 T^{3} + 18858 T^{4} - 89324 T^{5} + 1376634 T^{6} - 11809064 T^{7} + 117094117 T^{8} - 511168338 T^{9} + 2073071593 T^{10} \))
$79$ (\( 1 + 12 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))(\( 1 + 4 T + 154 T^{2} + 316 T^{3} + 6241 T^{4} \))(\( 1 - 20 T + 427 T^{2} - 5424 T^{3} + 67690 T^{4} - 606328 T^{5} + 5347510 T^{6} - 33851184 T^{7} + 210527653 T^{8} - 779001620 T^{9} + 3077056399 T^{10} \))
$83$ (\( 1 + 2 T + 83 T^{2} \))(\( 1 - 4 T + 83 T^{2} \))(\( 1 + 8 T + 20 T^{2} + 664 T^{3} + 6889 T^{4} \))(\( 1 - 38 T + 903 T^{2} - 14840 T^{3} + 189778 T^{4} - 1919492 T^{5} + 15751574 T^{6} - 102232760 T^{7} + 516323661 T^{8} - 1803416198 T^{9} + 3939040643 T^{10} \))
$89$ (\( 1 - 6 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 + 4 T + 110 T^{2} + 356 T^{3} + 7921 T^{4} \))(\( 1 - 18 T + 389 T^{2} - 3736 T^{3} + 48658 T^{4} - 354540 T^{5} + 4330562 T^{6} - 29592856 T^{7} + 274232941 T^{8} - 1129360338 T^{9} + 5584059449 T^{10} \))
$97$ (\( 1 - T \))(\( 1 - T \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{5} \))
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