Properties

 Label 4006.2 Level 4006 Weight 2 Dimension 167166 Nonzero newspaces 8 Sturm bound 2.006e+06

Defining parameters

 Level: $$N$$ = $$4006 = 2 \cdot 2003$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Sturm bound: $$2006004$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4006))$$.

Total New Old
Modular forms 503503 167166 336337
Cusp forms 499500 167166 332334
Eisenstein series 4003 0 4003

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4006))$$

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
4006.2.a $$\chi_{4006}(1, \cdot)$$ 4006.2.a.a 1 1
4006.2.a.b 1
4006.2.a.c 1
4006.2.a.d 2
4006.2.a.e 2
4006.2.a.f 31
4006.2.a.g 40
4006.2.a.h 42
4006.2.a.i 46
4006.2.c $$\chi_{4006}(485, \cdot)$$ n/a 1002 6
4006.2.d $$\chi_{4006}(523, \cdot)$$ n/a 1670 10
4006.2.e $$\chi_{4006}(89, \cdot)$$ n/a 2004 12
4006.2.i $$\chi_{4006}(57, \cdot)$$ n/a 10020 60
4006.2.j $$\chi_{4006}(53, \cdot)$$ n/a 12024 72
4006.2.k $$\chi_{4006}(113, \cdot)$$ n/a 20040 120
4006.2.o $$\chi_{4006}(3, \cdot)$$ n/a 120240 720

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4006))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4006)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(2003))$$$$^{\oplus 2}$$

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ ($$1 + T$$)($$1 - T$$)($$1 - T$$)($$( 1 - T )^{2}$$)($$( 1 - T )^{2}$$)
$3$ ($$1 + 3 T^{2}$$)($$1 + 2 T + 3 T^{2}$$)($$1 - T + 3 T^{2}$$)($$1 + 4 T + 8 T^{2} + 12 T^{3} + 9 T^{4}$$)($$1 + 4 T^{2} + 9 T^{4}$$)
$5$ ($$1 + 3 T + 5 T^{2}$$)($$1 + 3 T + 5 T^{2}$$)($$1 - 2 T + 5 T^{2}$$)($$( 1 - T + 5 T^{2} )^{2}$$)($$( 1 + T + 5 T^{2} )^{2}$$)
$7$ ($$1 + 2 T + 7 T^{2}$$)($$1 + 2 T + 7 T^{2}$$)($$1 + 2 T + 7 T^{2}$$)($$1 + 4 T + 16 T^{2} + 28 T^{3} + 49 T^{4}$$)($$1 + 4 T + 16 T^{2} + 28 T^{3} + 49 T^{4}$$)
$11$ ($$1 + 11 T^{2}$$)($$1 + 4 T + 11 T^{2}$$)($$1 + 2 T + 11 T^{2}$$)($$1 - 4 T + 18 T^{2} - 44 T^{3} + 121 T^{4}$$)($$( 1 + 2 T + 11 T^{2} )^{2}$$)
$13$ ($$1 + 4 T + 13 T^{2}$$)($$1 + 4 T + 13 T^{2}$$)($$1 + 5 T + 13 T^{2}$$)($$1 + 8 T^{2} + 169 T^{4}$$)($$1 - 8 T + 40 T^{2} - 104 T^{3} + 169 T^{4}$$)
$17$ ($$1 + 4 T + 17 T^{2}$$)($$1 + 6 T + 17 T^{2}$$)($$1 + 17 T^{2}$$)($$( 1 + 6 T + 17 T^{2} )^{2}$$)($$( 1 - 4 T + 17 T^{2} )^{2}$$)
$19$ ($$1 + 2 T + 19 T^{2}$$)($$1 + 2 T + 19 T^{2}$$)($$1 + 4 T + 19 T^{2}$$)($$1 - 4 T + 40 T^{2} - 76 T^{3} + 361 T^{4}$$)($$1 - 4 T + 40 T^{2} - 76 T^{3} + 361 T^{4}$$)
$23$ ($$1 - 2 T + 23 T^{2}$$)($$1 + 4 T + 23 T^{2}$$)($$1 + 2 T + 23 T^{2}$$)($$1 + 28 T^{2} + 529 T^{4}$$)($$1 + 4 T + 32 T^{2} + 92 T^{3} + 529 T^{4}$$)
$29$ ($$1 + 5 T + 29 T^{2}$$)($$1 + 5 T + 29 T^{2}$$)($$1 + 2 T + 29 T^{2}$$)($$( 1 + 3 T + 29 T^{2} )^{2}$$)($$( 1 + 5 T + 29 T^{2} )^{2}$$)
$31$ ($$1 + 2 T + 31 T^{2}$$)($$1 + 2 T + 31 T^{2}$$)($$1 - 2 T + 31 T^{2}$$)($$1 + 12 T + 90 T^{2} + 372 T^{3} + 961 T^{4}$$)($$1 + 4 T + 58 T^{2} + 124 T^{3} + 961 T^{4}$$)
$37$ ($$1 + 7 T + 37 T^{2}$$)($$1 + 3 T + 37 T^{2}$$)($$1 + 2 T + 37 T^{2}$$)($$1 - 14 T + 115 T^{2} - 518 T^{3} + 1369 T^{4}$$)($$( 1 + 11 T + 37 T^{2} )^{2}$$)
$41$ ($$1 + 12 T + 41 T^{2}$$)($$1 - 12 T + 41 T^{2}$$)($$1 - 8 T + 41 T^{2}$$)($$1 - 16 T^{2} + 1681 T^{4}$$)($$1 - 16 T^{2} + 1681 T^{4}$$)
$43$ ($$1 + 4 T + 43 T^{2}$$)($$1 + 8 T + 43 T^{2}$$)($$1 + 10 T + 43 T^{2}$$)($$1 - 4 T + 58 T^{2} - 172 T^{3} + 1849 T^{4}$$)($$1 + 4 T + 18 T^{2} + 172 T^{3} + 1849 T^{4}$$)
$47$ ($$1 + 47 T^{2}$$)($$1 + 8 T + 47 T^{2}$$)($$1 - 13 T + 47 T^{2}$$)($$1 - 20 T + 186 T^{2} - 940 T^{3} + 2209 T^{4}$$)($$( 1 - 6 T + 47 T^{2} )^{2}$$)
$53$ ($$1 + 12 T + 53 T^{2}$$)($$1 + 6 T + 53 T^{2}$$)($$1 + 6 T + 53 T^{2}$$)($$1 + 4 T + 38 T^{2} + 212 T^{3} + 2809 T^{4}$$)($$1 - 8 T + 114 T^{2} - 424 T^{3} + 2809 T^{4}$$)
$59$ ($$1 - 8 T + 59 T^{2}$$)($$1 - 10 T + 59 T^{2}$$)($$1 + 3 T + 59 T^{2}$$)($$1 + 4 T + 90 T^{2} + 236 T^{3} + 3481 T^{4}$$)($$1 - 10 T^{2} + 3481 T^{4}$$)
$61$ ($$1 + T + 61 T^{2}$$)($$1 - 3 T + 61 T^{2}$$)($$1 - 4 T + 61 T^{2}$$)($$1 + 14 T + 139 T^{2} + 854 T^{3} + 3721 T^{4}$$)($$1 - 6 T + 3 T^{2} - 366 T^{3} + 3721 T^{4}$$)
$67$ ($$1 + 15 T + 67 T^{2}$$)($$1 + 13 T + 67 T^{2}$$)($$1 + 8 T + 67 T^{2}$$)($$1 + 14 T + 151 T^{2} + 938 T^{3} + 4489 T^{4}$$)($$1 + 14 T + 151 T^{2} + 938 T^{3} + 4489 T^{4}$$)
$71$ ($$1 - 12 T + 71 T^{2}$$)($$1 + 4 T + 71 T^{2}$$)($$1 + 71 T^{2}$$)($$1 + 8 T + 140 T^{2} + 568 T^{3} + 5041 T^{4}$$)($$1 + 16 T + 204 T^{2} + 1136 T^{3} + 5041 T^{4}$$)
$73$ ($$1 - 3 T + 73 T^{2}$$)($$1 + 9 T + 73 T^{2}$$)($$1 + T + 73 T^{2}$$)($$( 1 - 7 T + 73 T^{2} )^{2}$$)($$1 - 6 T + 147 T^{2} - 438 T^{3} + 5329 T^{4}$$)
$79$ ($$1 + 5 T + 79 T^{2}$$)($$1 - 13 T + 79 T^{2}$$)($$1 + 17 T + 79 T^{2}$$)($$1 - 10 T + 175 T^{2} - 790 T^{3} + 6241 T^{4}$$)($$1 + 2 T + 31 T^{2} + 158 T^{3} + 6241 T^{4}$$)
$83$ ($$1 - 15 T + 83 T^{2}$$)($$1 - T + 83 T^{2}$$)($$1 - 16 T + 83 T^{2}$$)($$( 1 - T + 83 T^{2} )^{2}$$)($$1 + 6 T + 103 T^{2} + 498 T^{3} + 6889 T^{4}$$)
$89$ ($$1 + 13 T + 89 T^{2}$$)($$1 - 15 T + 89 T^{2}$$)($$1 + 2 T + 89 T^{2}$$)($$1 + 10 T + 131 T^{2} + 890 T^{3} + 7921 T^{4}$$)($$1 - 14 T + 219 T^{2} - 1246 T^{3} + 7921 T^{4}$$)
$97$ ($$1 + 8 T + 97 T^{2}$$)($$1 + 2 T + 97 T^{2}$$)($$1 - 14 T + 97 T^{2}$$)($$1 + 12 T + 228 T^{2} + 1164 T^{3} + 9409 T^{4}$$)($$1 + 24 T + 320 T^{2} + 2328 T^{3} + 9409 T^{4}$$)