Properties

Label 4031.2
Level 4031
Weight 2
Dimension 670819
Nonzero newspaces 24
Sturm bound 2704800

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 4031 = 29 \cdot 139 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(2704800\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4031))\).

Total New Old
Modular forms 680064 678219 1845
Cusp forms 672337 670819 1518
Eisenstein series 7727 7400 327

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4031))\)

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
4031.2.a \(\chi_{4031}(1, \cdot)\) 4031.2.a.a 2 1
4031.2.a.b 59
4031.2.a.c 61
4031.2.a.d 98
4031.2.a.e 103
4031.2.b \(\chi_{4031}(1391, \cdot)\) n/a 344 1
4031.2.e \(\chi_{4031}(320, \cdot)\) n/a 652 2
4031.2.g \(\chi_{4031}(3057, \cdot)\) n/a 696 2
4031.2.j \(\chi_{4031}(1710, \cdot)\) n/a 696 2
4031.2.k \(\chi_{4031}(140, \cdot)\) n/a 2076 6
4031.2.l \(\chi_{4031}(1433, \cdot)\) n/a 1392 4
4031.2.p \(\chi_{4031}(557, \cdot)\) n/a 2064 6
4031.2.q \(\chi_{4031}(181, \cdot)\) n/a 4176 12
4031.2.r \(\chi_{4031}(175, \cdot)\) n/a 7216 22
4031.2.s \(\chi_{4031}(416, \cdot)\) n/a 4176 12
4031.2.u \(\chi_{4031}(42, \cdot)\) n/a 4176 12
4031.2.z \(\chi_{4031}(57, \cdot)\) n/a 7656 22
4031.2.ba \(\chi_{4031}(30, \cdot)\) n/a 14344 44
4031.2.bc \(\chi_{4031}(43, \cdot)\) n/a 8352 24
4031.2.bd \(\chi_{4031}(75, \cdot)\) n/a 15312 44
4031.2.bf \(\chi_{4031}(28, \cdot)\) n/a 15312 44
4031.2.bi \(\chi_{4031}(36, \cdot)\) n/a 45936 132
4031.2.bk \(\chi_{4031}(12, \cdot)\) n/a 30624 88
4031.2.bl \(\chi_{4031}(6, \cdot)\) n/a 45936 132
4031.2.bo \(\chi_{4031}(7, \cdot)\) n/a 91872 264
4031.2.bq \(\chi_{4031}(8, \cdot)\) n/a 91872 264
4031.2.bt \(\chi_{4031}(4, \cdot)\) n/a 91872 264
4031.2.bu \(\chi_{4031}(2, \cdot)\) n/a 183744 528

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4031))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4031)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(139))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 - 2 T + 3 T^{2} - 4 T^{3} + 4 T^{4} \))
$3$ (\( 1 - 2 T + 5 T^{2} - 6 T^{3} + 9 T^{4} \))
$5$ (\( ( 1 - 2 T + 5 T^{2} )^{2} \))
$7$ (\( 1 + 2 T + 7 T^{2} + 14 T^{3} + 49 T^{4} \))
$11$ (\( ( 1 + 11 T^{2} )^{2} \))
$13$ (\( ( 1 - 5 T + 13 T^{2} )^{2} \))
$17$ (\( 1 - 6 T + 41 T^{2} - 102 T^{3} + 289 T^{4} \))
$19$ (\( 1 + 2 T + 21 T^{2} + 38 T^{3} + 361 T^{4} \))
$23$ (\( 1 - 12 T + 74 T^{2} - 276 T^{3} + 529 T^{4} \))
$29$ (\( ( 1 - T )^{2} \))
$31$ (\( 1 - 4 T + 58 T^{2} - 124 T^{3} + 961 T^{4} \))
$37$ (\( 1 + 2 T^{2} + 1369 T^{4} \))
$41$ (\( ( 1 - 2 T + 41 T^{2} )^{2} \))
$43$ (\( 1 + 2 T + 85 T^{2} + 86 T^{3} + 1849 T^{4} \))
$47$ (\( 1 - 4 T + 90 T^{2} - 188 T^{3} + 2209 T^{4} \))
$53$ (\( 1 - 8 T + 114 T^{2} - 424 T^{3} + 2809 T^{4} \))
$59$ (\( 1 + 12 T + 122 T^{2} + 708 T^{3} + 3481 T^{4} \))
$61$ (\( 1 - 2 T + 25 T^{2} - 122 T^{3} + 3721 T^{4} \))
$67$ (\( 1 + 2 T + 7 T^{2} + 134 T^{3} + 4489 T^{4} \))
$71$ (\( 1 + 6 T + 23 T^{2} + 426 T^{3} + 5041 T^{4} \))
$73$ (\( 1 - 6 T + 105 T^{2} - 438 T^{3} + 5329 T^{4} \))
$79$ (\( 1 - 12 T + 122 T^{2} - 948 T^{3} + 6241 T^{4} \))
$83$ (\( ( 1 + 7 T + 83 T^{2} )^{2} \))
$89$ (\( 1 + 28 T + 366 T^{2} + 2492 T^{3} + 7921 T^{4} \))
$97$ (\( 1 - 10 T + 201 T^{2} - 970 T^{3} + 9409 T^{4} \))
show more
show less