Properties

Label 5077.2
Level 5077
Weight 2
Dimension 1071460
Nonzero newspaces 16
Sturm bound 4295988

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Defining parameters

Level: \( N \) = \( 5077 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(4295988\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5077))\).

Total New Old
Modular forms 1076535 1076535 0
Cusp forms 1071460 1071460 0
Eisenstein series 5075 5075 0

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5077))\)

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
5077.2.a \(\chi_{5077}(1, \cdot)\) 5077.2.a.a 1 1
5077.2.a.b 205
5077.2.a.c 216
5077.2.b \(\chi_{5077}(5076, \cdot)\) n/a 422 1
5077.2.c \(\chi_{5077}(1629, \cdot)\) n/a 842 2
5077.2.e \(\chi_{5077}(1630, \cdot)\) n/a 844 2
5077.2.f \(\chi_{5077}(360, \cdot)\) n/a 2526 6
5077.2.h \(\chi_{5077}(2402, \cdot)\) n/a 2532 6
5077.2.i \(\chi_{5077}(382, \cdot)\) n/a 7596 18
5077.2.k \(\chi_{5077}(321, \cdot)\) n/a 19366 46
5077.2.l \(\chi_{5077}(21, \cdot)\) n/a 7614 18
5077.2.m \(\chi_{5077}(25, \cdot)\) n/a 19412 46
5077.2.o \(\chi_{5077}(89, \cdot)\) n/a 38732 92
5077.2.q \(\chi_{5077}(22, \cdot)\) n/a 38824 92
5077.2.r \(\chi_{5077}(9, \cdot)\) n/a 116196 276
5077.2.t \(\chi_{5077}(3, \cdot)\) n/a 116472 276
5077.2.u \(\chi_{5077}(7, \cdot)\) n/a 349416 828
5077.2.w \(\chi_{5077}(4, \cdot)\) n/a 350244 828

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

Hecke Characteristic Polynomials

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