# Properties

 Label 6046.2 Level 6046 Weight 2 Dimension 380771 Nonzero newspaces 2 Sturm bound 4.56926e+06

## Defining parameters

 Level: $$N$$ = $$6046\( 6046 = 2 \cdot 3023$$ \) Weight: $$k$$ = $$2$$ Nonzero newspaces: $$2$$ Sturm bound: $$4569264$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(6046))$$.

Total New Old
Modular forms 1145338 380771 764567
Cusp forms 1139295 380771 758524
Eisenstein series 6043 0 6043

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(6046))$$

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
6046.2.a $$\chi_{6046}(1, \cdot)$$ 6046.2.a.a 1 1
6046.2.a.b 1
6046.2.a.c 2
6046.2.a.d 55
6046.2.a.e 56
6046.2.a.f 67
6046.2.a.g 69
6046.2.c $$\chi_{6046}(3, \cdot)$$ n/a 380520 1510

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(6046))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(6046)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(3023))$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 + T$$)($$1 + T$$)($$( 1 - T )^{2}$$)
$3$ ($$1 - 2 T + 3 T^{2}$$)($$1 - 2 T + 3 T^{2}$$)($$1 + 3 T + 7 T^{2} + 9 T^{3} + 9 T^{4}$$)
$5$ ($$1 + 2 T + 5 T^{2}$$)($$1 + 2 T + 5 T^{2}$$)($$( 1 + 3 T + 5 T^{2} )^{2}$$)
$7$ ($$1 - 2 T + 7 T^{2}$$)($$1 - 2 T + 7 T^{2}$$)($$1 + 5 T + 19 T^{2} + 35 T^{3} + 49 T^{4}$$)
$11$ ($$1 + 5 T + 11 T^{2}$$)($$1 + 3 T + 11 T^{2}$$)($$1 + 3 T + 23 T^{2} + 33 T^{3} + 121 T^{4}$$)
$13$ ($$1 + 2 T + 13 T^{2}$$)($$1 - 2 T + 13 T^{2}$$)($$1 + 8 T + 37 T^{2} + 104 T^{3} + 169 T^{4}$$)
$17$ ($$1 - 4 T + 17 T^{2}$$)($$1 + 17 T^{2}$$)($$( 1 + 5 T + 17 T^{2} )^{2}$$)
$19$ ($$1 + 6 T + 19 T^{2}$$)($$1 - 6 T + 19 T^{2}$$)($$1 + 11 T + 67 T^{2} + 209 T^{3} + 361 T^{4}$$)
$23$ ($$1 - 6 T + 23 T^{2}$$)($$1 + 6 T + 23 T^{2}$$)($$1 + 8 T + 57 T^{2} + 184 T^{3} + 529 T^{4}$$)
$29$ ($$1 + 3 T + 29 T^{2}$$)($$1 - T + 29 T^{2}$$)($$1 - 2 T + 54 T^{2} - 58 T^{3} + 841 T^{4}$$)
$31$ ($$1 - 9 T + 31 T^{2}$$)($$1 - 3 T + 31 T^{2}$$)($$1 + 42 T^{2} + 961 T^{4}$$)
$37$ ($$1 - 5 T + 37 T^{2}$$)($$1 - T + 37 T^{2}$$)($$1 + 6 T + 63 T^{2} + 222 T^{3} + 1369 T^{4}$$)
$41$ ($$1 - 6 T + 41 T^{2}$$)($$1 + 10 T + 41 T^{2}$$)($$1 + 13 T + 93 T^{2} + 533 T^{3} + 1681 T^{4}$$)
$43$ ($$1 + 7 T + 43 T^{2}$$)($$1 + T + 43 T^{2}$$)($$1 - 3 T + 77 T^{2} - 129 T^{3} + 1849 T^{4}$$)
$47$ ($$1 - 4 T + 47 T^{2}$$)($$1 + 8 T + 47 T^{2}$$)($$1 + 6 T + 83 T^{2} + 282 T^{3} + 2209 T^{4}$$)
$53$ ($$1 - 10 T + 53 T^{2}$$)($$1 + 6 T + 53 T^{2}$$)($$1 - T + 105 T^{2} - 53 T^{3} + 2809 T^{4}$$)
$59$ ($$1 + 4 T + 59 T^{2}$$)($$1 - 4 T + 59 T^{2}$$)($$1 + 8 T + 89 T^{2} + 472 T^{3} + 3481 T^{4}$$)
$61$ ($$1 - 5 T + 61 T^{2}$$)($$1 - T + 61 T^{2}$$)($$1 + 7 T + 103 T^{2} + 427 T^{3} + 3721 T^{4}$$)
$67$ ($$1 + 2 T + 67 T^{2}$$)($$1 + 2 T + 67 T^{2}$$)($$( 1 + 8 T + 67 T^{2} )^{2}$$)
$71$ ($$1 - 10 T + 71 T^{2}$$)($$1 - 2 T + 71 T^{2}$$)($$1 - 6 T + 106 T^{2} - 426 T^{3} + 5041 T^{4}$$)
$73$ ($$1 + 4 T + 73 T^{2}$$)($$1 - 16 T + 73 T^{2}$$)($$1 + 66 T^{2} + 5329 T^{4}$$)
$79$ ($$1 + 11 T + 79 T^{2}$$)($$1 + T + 79 T^{2}$$)($$1 - 10 T + 163 T^{2} - 790 T^{3} + 6241 T^{4}$$)
$83$ ($$1 - 2 T + 83 T^{2}$$)($$1 + 14 T + 83 T^{2}$$)($$1 + 8 T + 102 T^{2} + 664 T^{3} + 6889 T^{4}$$)
$89$ ($$1 - 18 T + 89 T^{2}$$)($$1 + 6 T + 89 T^{2}$$)($$1 + 158 T^{2} + 7921 T^{4}$$)
$97$ ($$1 - 3 T + 97 T^{2}$$)($$1 - 3 T + 97 T^{2}$$)($$1 + 4 T + 178 T^{2} + 388 T^{3} + 9409 T^{4}$$)