Properties

Label 6013.2
Level 6013
Weight 2
Dimension 1409979
Nonzero newspaces 40
Sturm bound 5903040

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Defining parameters

Level: \( N \) = \( 6013 = 7 \cdot 859 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(5903040\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6013))\).

Total New Old
Modular forms 1480908 1418551 62357
Cusp forms 1470613 1409979 60634
Eisenstein series 10295 8572 1723

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6013))\)

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
6013.2.a \(\chi_{6013}(1, \cdot)\) 6013.2.a.a 1 1
6013.2.a.b 1
6013.2.a.c 104
6013.2.a.d 104
6013.2.a.e 109
6013.2.a.f 110
6013.2.c \(\chi_{6013}(6012, \cdot)\) n/a 570 1
6013.2.e \(\chi_{6013}(1719, \cdot)\) n/a 1144 2
6013.2.f \(\chi_{6013}(260, \cdot)\) n/a 860 2
6013.2.g \(\chi_{6013}(1978, \cdot)\) n/a 1142 2
6013.2.h \(\chi_{6013}(2837, \cdot)\) n/a 1142 2
6013.2.j \(\chi_{6013}(2838, \cdot)\) n/a 1142 2
6013.2.n \(\chi_{6013}(1979, \cdot)\) n/a 1142 2
6013.2.o \(\chi_{6013}(3435, \cdot)\) n/a 1144 2
6013.2.p \(\chi_{6013}(4556, \cdot)\) n/a 1144 2
6013.2.u \(\chi_{6013}(169, \cdot)\) n/a 4300 10
6013.2.v \(\chi_{6013}(463, \cdot)\) n/a 5160 12
6013.2.x \(\chi_{6013}(846, \cdot)\) n/a 5700 10
6013.2.ba \(\chi_{6013}(335, \cdot)\) n/a 6840 12
6013.2.bc \(\chi_{6013}(46, \cdot)\) n/a 11420 20
6013.2.bd \(\chi_{6013}(361, \cdot)\) n/a 11420 20
6013.2.be \(\chi_{6013}(88, \cdot)\) n/a 11440 20
6013.2.bf \(\chi_{6013}(43, \cdot)\) n/a 8600 20
6013.2.bg \(\chi_{6013}(144, \cdot)\) n/a 13704 24
6013.2.bh \(\chi_{6013}(277, \cdot)\) n/a 13704 24
6013.2.bi \(\chi_{6013}(120, \cdot)\) n/a 10320 24
6013.2.bj \(\chi_{6013}(100, \cdot)\) n/a 13728 24
6013.2.bo \(\chi_{6013}(66, \cdot)\) n/a 11440 20
6013.2.bp \(\chi_{6013}(195, \cdot)\) n/a 11440 20
6013.2.bq \(\chi_{6013}(19, \cdot)\) n/a 11420 20
6013.2.bu \(\chi_{6013}(313, \cdot)\) n/a 11420 20
6013.2.ca \(\chi_{6013}(629, \cdot)\) n/a 13728 24
6013.2.cb \(\chi_{6013}(10, \cdot)\) n/a 13728 24
6013.2.cc \(\chi_{6013}(402, \cdot)\) n/a 13704 24
6013.2.cg \(\chi_{6013}(12, \cdot)\) n/a 13704 24
6013.2.ci \(\chi_{6013}(36, \cdot)\) n/a 51600 120
6013.2.ck \(\chi_{6013}(27, \cdot)\) n/a 68400 120
6013.2.cm \(\chi_{6013}(22, \cdot)\) n/a 103200 240
6013.2.cn \(\chi_{6013}(74, \cdot)\) n/a 137280 240
6013.2.co \(\chi_{6013}(25, \cdot)\) n/a 137040 240
6013.2.cp \(\chi_{6013}(4, \cdot)\) n/a 137040 240
6013.2.cr \(\chi_{6013}(3, \cdot)\) n/a 137040 240
6013.2.cv \(\chi_{6013}(40, \cdot)\) n/a 137040 240
6013.2.cw \(\chi_{6013}(55, \cdot)\) n/a 137280 240
6013.2.cx \(\chi_{6013}(75, \cdot)\) n/a 137280 240

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6013))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6013)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(859))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

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