Properties

Label 6019.2
Level 6019
Weight 2
Dimension 1477625
Nonzero newspaces 60
Sturm bound 6002304

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Defining parameters

Level: \( N \) = \( 6019 = 13 \cdot 463 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(6002304\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6019))\).

Total New Old
Modular forms 1506120 1487769 18351
Cusp forms 1495033 1477625 17408
Eisenstein series 11087 10144 943

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6019))\)

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
6019.2.a \(\chi_{6019}(1, \cdot)\) 6019.2.a.a 1 1
6019.2.a.b 101
6019.2.a.c 108
6019.2.a.d 123
6019.2.a.e 130
6019.2.c \(\chi_{6019}(1390, \cdot)\) n/a 538 1
6019.2.e \(\chi_{6019}(484, \cdot)\) n/a 1078 2
6019.2.f \(\chi_{6019}(1873, \cdot)\) n/a 928 2
6019.2.g \(\chi_{6019}(464, \cdot)\) n/a 1080 2
6019.2.h \(\chi_{6019}(2336, \cdot)\) n/a 1078 2
6019.2.i \(\chi_{6019}(1851, \cdot)\) n/a 1076 2
6019.2.l \(\chi_{6019}(1830, \cdot)\) n/a 1078 2
6019.2.p \(\chi_{6019}(927, \cdot)\) n/a 1076 2
6019.2.q \(\chi_{6019}(441, \cdot)\) n/a 1080 2
6019.2.r \(\chi_{6019}(4651, \cdot)\) n/a 1078 2
6019.2.w \(\chi_{6019}(118, \cdot)\) n/a 2784 6
6019.2.x \(\chi_{6019}(1288, \cdot)\) n/a 4640 10
6019.2.y \(\chi_{6019}(1874, \cdot)\) n/a 2156 4
6019.2.bc \(\chi_{6019}(462, \cdot)\) n/a 2160 4
6019.2.bd \(\chi_{6019}(1411, \cdot)\) n/a 2156 4
6019.2.be \(\chi_{6019}(905, \cdot)\) n/a 2160 4
6019.2.bh \(\chi_{6019}(1156, \cdot)\) n/a 3228 6
6019.2.bj \(\chi_{6019}(653, \cdot)\) n/a 6468 12
6019.2.bk \(\chi_{6019}(230, \cdot)\) n/a 6480 12
6019.2.bl \(\chi_{6019}(196, \cdot)\) n/a 5568 12
6019.2.bm \(\chi_{6019}(178, \cdot)\) n/a 6468 12
6019.2.bo \(\chi_{6019}(337, \cdot)\) n/a 5380 10
6019.2.br \(\chi_{6019}(177, \cdot)\) n/a 6456 12
6019.2.bs \(\chi_{6019}(133, \cdot)\) n/a 10780 20
6019.2.bt \(\chi_{6019}(55, \cdot)\) n/a 10800 20
6019.2.bu \(\chi_{6019}(833, \cdot)\) n/a 9280 20
6019.2.bv \(\chi_{6019}(68, \cdot)\) n/a 10780 20
6019.2.ca \(\chi_{6019}(641, \cdot)\) n/a 6468 12
6019.2.cb \(\chi_{6019}(714, \cdot)\) n/a 6480 12
6019.2.cc \(\chi_{6019}(693, \cdot)\) n/a 6480 12
6019.2.cg \(\chi_{6019}(251, \cdot)\) n/a 6468 12
6019.2.cj \(\chi_{6019}(216, \cdot)\) n/a 10760 20
6019.2.co \(\chi_{6019}(36, \cdot)\) n/a 10780 20
6019.2.cp \(\chi_{6019}(77, \cdot)\) n/a 10800 20
6019.2.cq \(\chi_{6019}(134, \cdot)\) n/a 10800 20
6019.2.cu \(\chi_{6019}(95, \cdot)\) n/a 10780 20
6019.2.cw \(\chi_{6019}(66, \cdot)\) n/a 27840 60
6019.2.cy \(\chi_{6019}(281, \cdot)\) n/a 12960 24
6019.2.cz \(\chi_{6019}(145, \cdot)\) n/a 12936 24
6019.2.da \(\chi_{6019}(345, \cdot)\) n/a 12960 24
6019.2.de \(\chi_{6019}(730, \cdot)\) n/a 12936 24
6019.2.dg \(\chi_{6019}(148, \cdot)\) n/a 21600 40
6019.2.dh \(\chi_{6019}(305, \cdot)\) n/a 21600 40
6019.2.di \(\chi_{6019}(6, \cdot)\) n/a 21560 40
6019.2.dm \(\chi_{6019}(93, \cdot)\) n/a 21560 40
6019.2.do \(\chi_{6019}(64, \cdot)\) n/a 32280 60
6019.2.dq \(\chi_{6019}(9, \cdot)\) n/a 64680 120
6019.2.dr \(\chi_{6019}(79, \cdot)\) n/a 55680 120
6019.2.ds \(\chi_{6019}(100, \cdot)\) n/a 64800 120
6019.2.dt \(\chi_{6019}(29, \cdot)\) n/a 64680 120
6019.2.du \(\chi_{6019}(44, \cdot)\) n/a 64560 120
6019.2.dx \(\chi_{6019}(30, \cdot)\) n/a 64680 120
6019.2.eb \(\chi_{6019}(49, \cdot)\) n/a 64800 120
6019.2.ec \(\chi_{6019}(25, \cdot)\) n/a 64800 120
6019.2.ed \(\chi_{6019}(4, \cdot)\) n/a 64680 120
6019.2.ei \(\chi_{6019}(20, \cdot)\) n/a 129360 240
6019.2.em \(\chi_{6019}(11, \cdot)\) n/a 129360 240
6019.2.en \(\chi_{6019}(7, \cdot)\) n/a 129600 240
6019.2.eo \(\chi_{6019}(5, \cdot)\) n/a 129600 240

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6019))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6019)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(463))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T^{2} \))
$3$ (\( 1 + 3 T^{2} \))
$5$ (\( 1 - 3 T + 5 T^{2} \))
$7$ (\( 1 + 3 T + 7 T^{2} \))
$11$ (\( 1 + T + 11 T^{2} \))
$13$ (\( 1 - T \))
$17$ (\( 1 - 2 T + 17 T^{2} \))
$19$ (\( 1 + T + 19 T^{2} \))
$23$ (\( 1 - 2 T + 23 T^{2} \))
$29$ (\( 1 - 5 T + 29 T^{2} \))
$31$ (\( 1 - 4 T + 31 T^{2} \))
$37$ (\( 1 + 9 T + 37 T^{2} \))
$41$ (\( 1 - 2 T + 41 T^{2} \))
$43$ (\( 1 + 4 T + 43 T^{2} \))
$47$ (\( 1 + 47 T^{2} \))
$53$ (\( 1 - 6 T + 53 T^{2} \))
$59$ (\( 1 - 10 T + 59 T^{2} \))
$61$ (\( 1 + 5 T + 61 T^{2} \))
$67$ (\( 1 - 12 T + 67 T^{2} \))
$71$ (\( 1 + 7 T + 71 T^{2} \))
$73$ (\( 1 + 6 T + 73 T^{2} \))
$79$ (\( 1 - 5 T + 79 T^{2} \))
$83$ (\( 1 + 4 T + 83 T^{2} \))
$89$ (\( 1 + 8 T + 89 T^{2} \))
$97$ (\( 1 + 2 T + 97 T^{2} \))
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