Properties

Label 6.6.a
Level 6
Weight 6
Character orbit a
Rep. character \(\chi_{6}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 6.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 7 1 6
Cusp forms 3 1 2
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.

\(2\)\(3\)FrickeDim.
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(1\)

Trace form

\( q + 4q^{2} - 9q^{3} + 16q^{4} - 66q^{5} - 36q^{6} + 176q^{7} + 64q^{8} + 81q^{9} + O(q^{10}) \) \( q + 4q^{2} - 9q^{3} + 16q^{4} - 66q^{5} - 36q^{6} + 176q^{7} + 64q^{8} + 81q^{9} - 264q^{10} - 60q^{11} - 144q^{12} - 658q^{13} + 704q^{14} + 594q^{15} + 256q^{16} - 414q^{17} + 324q^{18} + 956q^{19} - 1056q^{20} - 1584q^{21} - 240q^{22} + 600q^{23} - 576q^{24} + 1231q^{25} - 2632q^{26} - 729q^{27} + 2816q^{28} + 5574q^{29} + 2376q^{30} - 3592q^{31} + 1024q^{32} + 540q^{33} - 1656q^{34} - 11616q^{35} + 1296q^{36} - 8458q^{37} + 3824q^{38} + 5922q^{39} - 4224q^{40} + 19194q^{41} - 6336q^{42} + 13316q^{43} - 960q^{44} - 5346q^{45} + 2400q^{46} - 19680q^{47} - 2304q^{48} + 14169q^{49} + 4924q^{50} + 3726q^{51} - 10528q^{52} - 31266q^{53} - 2916q^{54} + 3960q^{55} + 11264q^{56} - 8604q^{57} + 22296q^{58} + 26340q^{59} + 9504q^{60} - 31090q^{61} - 14368q^{62} + 14256q^{63} + 4096q^{64} + 43428q^{65} + 2160q^{66} - 16804q^{67} - 6624q^{68} - 5400q^{69} - 46464q^{70} + 6120q^{71} + 5184q^{72} - 25558q^{73} - 33832q^{74} - 11079q^{75} + 15296q^{76} - 10560q^{77} + 23688q^{78} + 74408q^{79} - 16896q^{80} + 6561q^{81} + 76776q^{82} - 6468q^{83} - 25344q^{84} + 27324q^{85} + 53264q^{86} - 50166q^{87} - 3840q^{88} - 32742q^{89} - 21384q^{90} - 115808q^{91} + 9600q^{92} + 32328q^{93} - 78720q^{94} - 63096q^{95} - 9216q^{96} + 166082q^{97} + 56676q^{98} - 4860q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
6.6.a.a \(1\) \(0.962\) \(\Q\) None \(4\) \(-9\) \(-66\) \(176\) \(-\) \(+\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}-66q^{5}-6^{2}q^{6}+\cdots\)

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

\( S_{6}^{\mathrm{old}}(\Gamma_0(6)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 4 T \)
$3$ \( 1 + 9 T \)
$5$ \( 1 + 66 T + 3125 T^{2} \)
$7$ \( 1 - 176 T + 16807 T^{2} \)
$11$ \( 1 + 60 T + 161051 T^{2} \)
$13$ \( 1 + 658 T + 371293 T^{2} \)
$17$ \( 1 + 414 T + 1419857 T^{2} \)
$19$ \( 1 - 956 T + 2476099 T^{2} \)
$23$ \( 1 - 600 T + 6436343 T^{2} \)
$29$ \( 1 - 5574 T + 20511149 T^{2} \)
$31$ \( 1 + 3592 T + 28629151 T^{2} \)
$37$ \( 1 + 8458 T + 69343957 T^{2} \)
$41$ \( 1 - 19194 T + 115856201 T^{2} \)
$43$ \( 1 - 13316 T + 147008443 T^{2} \)
$47$ \( 1 + 19680 T + 229345007 T^{2} \)
$53$ \( 1 + 31266 T + 418195493 T^{2} \)
$59$ \( 1 - 26340 T + 714924299 T^{2} \)
$61$ \( 1 + 31090 T + 844596301 T^{2} \)
$67$ \( 1 + 16804 T + 1350125107 T^{2} \)
$71$ \( 1 - 6120 T + 1804229351 T^{2} \)
$73$ \( 1 + 25558 T + 2073071593 T^{2} \)
$79$ \( 1 - 74408 T + 3077056399 T^{2} \)
$83$ \( 1 + 6468 T + 3939040643 T^{2} \)
$89$ \( 1 + 32742 T + 5584059449 T^{2} \)
$97$ \( 1 - 166082 T + 8587340257 T^{2} \)
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