Properties

Label 4.6
Level 4
Weight 6
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4\( 4 = 2^{2} \) \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(4))\).

Total New Old
Modular forms 4 1 3
Cusp forms 1 1 0
Eisenstein series 3 0 3

Trace form

\( q - 12q^{3} + 54q^{5} - 88q^{7} - 99q^{9} + O(q^{10}) \) \( q - 12q^{3} + 54q^{5} - 88q^{7} - 99q^{9} + 540q^{11} - 418q^{13} - 648q^{15} + 594q^{17} + 836q^{19} + 1056q^{21} - 4104q^{23} - 209q^{25} + 4104q^{27} - 594q^{29} + 4256q^{31} - 6480q^{33} - 4752q^{35} - 298q^{37} + 5016q^{39} + 17226q^{41} - 12100q^{43} - 5346q^{45} - 1296q^{47} - 9063q^{49} - 7128q^{51} + 19494q^{53} + 29160q^{55} - 10032q^{57} - 7668q^{59} - 34738q^{61} + 8712q^{63} - 22572q^{65} + 21812q^{67} + 49248q^{69} - 46872q^{71} + 67562q^{73} + 2508q^{75} - 47520q^{77} - 76912q^{79} - 25191q^{81} + 67716q^{83} + 32076q^{85} + 7128q^{87} + 29754q^{89} + 36784q^{91} - 51072q^{93} + 45144q^{95} - 122398q^{97} - 53460q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
4.6.a \(\chi_{4}(1, \cdot)\) 4.6.a.a 1 1

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 + 12 T + 243 T^{2} \)
$5$ \( 1 - 54 T + 3125 T^{2} \)
$7$ \( 1 + 88 T + 16807 T^{2} \)
$11$ \( 1 - 540 T + 161051 T^{2} \)
$13$ \( 1 + 418 T + 371293 T^{2} \)
$17$ \( 1 - 594 T + 1419857 T^{2} \)
$19$ \( 1 - 836 T + 2476099 T^{2} \)
$23$ \( 1 + 4104 T + 6436343 T^{2} \)
$29$ \( 1 + 594 T + 20511149 T^{2} \)
$31$ \( 1 - 4256 T + 28629151 T^{2} \)
$37$ \( 1 + 298 T + 69343957 T^{2} \)
$41$ \( 1 - 17226 T + 115856201 T^{2} \)
$43$ \( 1 + 12100 T + 147008443 T^{2} \)
$47$ \( 1 + 1296 T + 229345007 T^{2} \)
$53$ \( 1 - 19494 T + 418195493 T^{2} \)
$59$ \( 1 + 7668 T + 714924299 T^{2} \)
$61$ \( 1 + 34738 T + 844596301 T^{2} \)
$67$ \( 1 - 21812 T + 1350125107 T^{2} \)
$71$ \( 1 + 46872 T + 1804229351 T^{2} \)
$73$ \( 1 - 67562 T + 2073071593 T^{2} \)
$79$ \( 1 + 76912 T + 3077056399 T^{2} \)
$83$ \( 1 - 67716 T + 3939040643 T^{2} \)
$89$ \( 1 - 29754 T + 5584059449 T^{2} \)
$97$ \( 1 + 122398 T + 8587340257 T^{2} \)
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