Properties

Label 6017.2
Level 6017
Weight 2
Dimension 1466189
Nonzero newspaces 32
Sturm bound 5984160

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Defining parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(5984160\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6017))\).

Total New Old
Modular forms 1501500 1476001 25499
Cusp forms 1490581 1466189 24392
Eisenstein series 10919 9812 1107

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6017))\)

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
6017.2.a \(\chi_{6017}(1, \cdot)\) 6017.2.a.a 1 1
6017.2.a.b 1
6017.2.a.c 106
6017.2.a.d 107
6017.2.a.e 119
6017.2.a.f 121
6017.2.d \(\chi_{6017}(6016, \cdot)\) n/a 546 1
6017.2.e \(\chi_{6017}(1134, \cdot)\) n/a 912 2
6017.2.f \(\chi_{6017}(548, \cdot)\) n/a 2184 4
6017.2.g \(\chi_{6017}(1682, \cdot)\) n/a 1092 2
6017.2.j \(\chi_{6017}(628, \cdot)\) n/a 2748 6
6017.2.k \(\chi_{6017}(546, \cdot)\) n/a 2184 4
6017.2.n \(\chi_{6017}(353, \cdot)\) n/a 5496 12
6017.2.o \(\chi_{6017}(538, \cdot)\) n/a 3276 6
6017.2.r \(\chi_{6017}(587, \cdot)\) n/a 4368 8
6017.2.s \(\chi_{6017}(716, \cdot)\) n/a 5472 12
6017.2.t \(\chi_{6017}(197, \cdot)\) n/a 6552 12
6017.2.y \(\chi_{6017}(41, \cdot)\) n/a 4368 8
6017.2.z \(\chi_{6017}(9, \cdot)\) n/a 13104 24
6017.2.ba \(\chi_{6017}(199, \cdot)\) n/a 10944 24
6017.2.bd \(\chi_{6017}(120, \cdot)\) n/a 6552 12
6017.2.be \(\chi_{6017}(350, \cdot)\) n/a 26208 48
6017.2.bh \(\chi_{6017}(365, \cdot)\) n/a 13104 24
6017.2.bk \(\chi_{6017}(692, \cdot)\) n/a 13104 24
6017.2.bl \(\chi_{6017}(100, \cdot)\) n/a 32976 72
6017.2.bm \(\chi_{6017}(14, \cdot)\) n/a 26208 48
6017.2.bp \(\chi_{6017}(28, \cdot)\) n/a 26208 48
6017.2.bs \(\chi_{6017}(65, \cdot)\) n/a 39312 72
6017.2.bt \(\chi_{6017}(47, \cdot)\) n/a 52416 96
6017.2.bu \(\chi_{6017}(39, \cdot)\) n/a 26208 48
6017.2.bx \(\chi_{6017}(34, \cdot)\) n/a 65664 144
6017.2.by \(\chi_{6017}(83, \cdot)\) n/a 52416 96
6017.2.cb \(\chi_{6017}(64, \cdot)\) n/a 157248 288
6017.2.cc \(\chi_{6017}(32, \cdot)\) n/a 78624 144
6017.2.cf \(\chi_{6017}(8, \cdot)\) n/a 157248 288
6017.2.ci \(\chi_{6017}(4, \cdot)\) n/a 314496 576
6017.2.cl \(\chi_{6017}(2, \cdot)\) n/a 314496 576

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6017))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6017)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(547))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T^{2} \))(\( 1 + 2 T^{2} \))
$3$ (\( 1 + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))
$5$ (\( 1 + 5 T^{2} \))(\( 1 - 4 T + 5 T^{2} \))
$7$ (\( 1 + 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))
$11$ (\( 1 + T \))(\( 1 - T \))
$13$ (\( 1 + 5 T + 13 T^{2} \))(\( 1 - T + 13 T^{2} \))
$17$ (\( 1 + 4 T + 17 T^{2} \))(\( 1 - 8 T + 17 T^{2} \))
$19$ (\( 1 + 7 T + 19 T^{2} \))(\( 1 + 5 T + 19 T^{2} \))
$23$ (\( 1 - 2 T + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))
$29$ (\( 1 + T + 29 T^{2} \))(\( 1 - 5 T + 29 T^{2} \))
$31$ (\( 1 - 4 T + 31 T^{2} \))(\( 1 - 10 T + 31 T^{2} \))
$37$ (\( 1 + 6 T + 37 T^{2} \))(\( 1 + 37 T^{2} \))
$41$ (\( 1 - 2 T + 41 T^{2} \))(\( 1 + 41 T^{2} \))
$43$ (\( 1 + 8 T + 43 T^{2} \))(\( 1 + 10 T + 43 T^{2} \))
$47$ (\( 1 + 9 T + 47 T^{2} \))(\( 1 + 9 T + 47 T^{2} \))
$53$ (\( 1 - 2 T + 53 T^{2} \))(\( 1 + 10 T + 53 T^{2} \))
$59$ (\( 1 + 6 T + 59 T^{2} \))(\( 1 + 14 T + 59 T^{2} \))
$61$ (\( 1 + 14 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))
$67$ (\( 1 + 5 T + 67 T^{2} \))(\( 1 + T + 67 T^{2} \))
$71$ (\( 1 - 10 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))
$73$ (\( 1 + 6 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))
$79$ (\( 1 + 6 T + 79 T^{2} \))(\( 1 - 4 T + 79 T^{2} \))
$83$ (\( 1 - 4 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))
$89$ (\( 1 - 8 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))
$97$ (\( 1 - 15 T + 97 T^{2} \))(\( 1 + 13 T + 97 T^{2} \))
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