Properties

Label 14.6.a
Level 14
Weight 6
Character orbit a
Rep. character \(\chi_{14}(1,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 2
Sturm bound 12
Trace bound 2

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Defining parameters

Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 14.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(14))\).

Total New Old
Modular forms 12 2 10
Cusp forms 8 2 6
Eisenstein series 4 0 4

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

\(2\)\(7\)FrickeDim.
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(2\)

Trace form

\( 2q + 18q^{3} + 32q^{4} + 94q^{5} - 8q^{6} - 322q^{9} + O(q^{10}) \) \( 2q + 18q^{3} + 32q^{4} + 94q^{5} - 8q^{6} - 322q^{9} - 296q^{10} - 676q^{11} + 288q^{12} + 290q^{13} - 392q^{14} + 920q^{15} + 512q^{16} - 232q^{17} - 144q^{18} + 2902q^{19} + 1504q^{20} + 98q^{21} - 16q^{22} - 2200q^{23} - 128q^{24} + 906q^{25} - 3512q^{26} - 7236q^{27} - 1880q^{29} - 3040q^{30} + 1484q^{31} - 6080q^{33} + 10736q^{34} + 3626q^{35} - 5152q^{36} + 23512q^{37} + 7848q^{38} + 3488q^{39} - 4736q^{40} - 8352q^{41} - 3528q^{42} + 11812q^{43} - 10816q^{44} - 13802q^{45} + 24800q^{46} - 2124q^{47} + 4608q^{48} + 4802q^{49} - 27824q^{50} - 4772q^{51} + 4640q^{52} - 51876q^{53} + 1936q^{54} - 31624q^{55} - 6272q^{56} + 24156q^{57} - 46448q^{58} + 6646q^{59} + 14720q^{60} + 58814q^{61} + 64912q^{62} + 1764q^{63} + 8192q^{64} + 46116q^{65} + 2560q^{66} - 5136q^{67} - 3712q^{68} - 26000q^{69} - 18424q^{70} + 65144q^{71} - 2304q^{72} - 58116q^{73} - 20592q^{74} + 15110q^{75} + 46432q^{76} + 196q^{77} - 32768q^{78} - 21880q^{79} + 24064q^{80} + 12638q^{81} - 83184q^{82} - 112258q^{83} + 1568q^{84} - 110212q^{85} + 17616q^{86} - 5308q^{87} - 256q^{88} + 18564q^{89} + 40888q^{90} + 43022q^{91} - 35200q^{92} - 2872q^{93} + 6000q^{94} + 63800q^{95} - 2048q^{96} + 3672q^{97} + 108908q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(14))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7
14.6.a.a \(1\) \(2.245\) \(\Q\) None \(-4\) \(10\) \(84\) \(49\) \(+\) \(-\) \(q-4q^{2}+10q^{3}+2^{4}q^{4}+84q^{5}-40q^{6}+\cdots\)
14.6.a.b \(1\) \(2.245\) \(\Q\) None \(4\) \(8\) \(10\) \(-49\) \(-\) \(+\) \(q+4q^{2}+8q^{3}+2^{4}q^{4}+10q^{5}+2^{5}q^{6}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(14))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(14)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 4 T \))(\( 1 - 4 T \))
$3$ (\( 1 - 10 T + 243 T^{2} \))(\( 1 - 8 T + 243 T^{2} \))
$5$ (\( 1 - 84 T + 3125 T^{2} \))(\( 1 - 10 T + 3125 T^{2} \))
$7$ (\( 1 - 49 T \))(\( 1 + 49 T \))
$11$ (\( 1 + 336 T + 161051 T^{2} \))(\( 1 + 340 T + 161051 T^{2} \))
$13$ (\( 1 - 584 T + 371293 T^{2} \))(\( 1 + 294 T + 371293 T^{2} \))
$17$ (\( 1 + 1458 T + 1419857 T^{2} \))(\( 1 - 1226 T + 1419857 T^{2} \))
$19$ (\( 1 - 470 T + 2476099 T^{2} \))(\( 1 - 2432 T + 2476099 T^{2} \))
$23$ (\( 1 + 4200 T + 6436343 T^{2} \))(\( 1 - 2000 T + 6436343 T^{2} \))
$29$ (\( 1 - 4866 T + 20511149 T^{2} \))(\( 1 + 6746 T + 20511149 T^{2} \))
$31$ (\( 1 + 7372 T + 28629151 T^{2} \))(\( 1 - 8856 T + 28629151 T^{2} \))
$37$ (\( 1 - 14330 T + 69343957 T^{2} \))(\( 1 - 9182 T + 69343957 T^{2} \))
$41$ (\( 1 - 6222 T + 115856201 T^{2} \))(\( 1 + 14574 T + 115856201 T^{2} \))
$43$ (\( 1 - 3704 T + 147008443 T^{2} \))(\( 1 - 8108 T + 147008443 T^{2} \))
$47$ (\( 1 + 1812 T + 229345007 T^{2} \))(\( 1 + 312 T + 229345007 T^{2} \))
$53$ (\( 1 + 37242 T + 418195493 T^{2} \))(\( 1 + 14634 T + 418195493 T^{2} \))
$59$ (\( 1 - 34302 T + 714924299 T^{2} \))(\( 1 + 27656 T + 714924299 T^{2} \))
$61$ (\( 1 - 24476 T + 844596301 T^{2} \))(\( 1 - 34338 T + 844596301 T^{2} \))
$67$ (\( 1 + 17452 T + 1350125107 T^{2} \))(\( 1 - 12316 T + 1350125107 T^{2} \))
$71$ (\( 1 - 28224 T + 1804229351 T^{2} \))(\( 1 - 36920 T + 1804229351 T^{2} \))
$73$ (\( 1 - 3602 T + 2073071593 T^{2} \))(\( 1 + 61718 T + 2073071593 T^{2} \))
$79$ (\( 1 - 42872 T + 3077056399 T^{2} \))(\( 1 + 64752 T + 3077056399 T^{2} \))
$83$ (\( 1 + 35202 T + 3939040643 T^{2} \))(\( 1 + 77056 T + 3939040643 T^{2} \))
$89$ (\( 1 - 26730 T + 5584059449 T^{2} \))(\( 1 + 8166 T + 5584059449 T^{2} \))
$97$ (\( 1 + 16978 T + 8587340257 T^{2} \))(\( 1 - 20650 T + 8587340257 T^{2} \))
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