# Properties

 Label 1005.2.c Level 1005 Weight 2 Character orbit c Rep. character $$\chi_{1005}(604,\cdot)$$ Character field $$\Q$$ Dimension 68 Newform subspaces 4 Sturm bound 272 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$1005 = 3 \cdot 5 \cdot 67$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 1005.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$5$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$272$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1005, [\chi])$$.

Total New Old
Modular forms 140 68 72
Cusp forms 132 68 64
Eisenstein series 8 0 8

## Trace form

 $$68q - 68q^{4} - 68q^{9} + O(q^{10})$$ $$68q - 68q^{4} - 68q^{9} - 12q^{10} + 24q^{14} - 4q^{15} + 68q^{16} + 8q^{20} + 8q^{21} - 4q^{25} - 40q^{26} - 8q^{29} - 16q^{30} + 40q^{34} + 20q^{35} + 68q^{36} - 16q^{39} + 28q^{40} - 16q^{41} - 48q^{44} + 40q^{46} - 92q^{49} + 8q^{50} - 8q^{51} + 48q^{55} + 16q^{59} - 8q^{60} - 16q^{61} - 44q^{64} + 52q^{65} - 8q^{66} + 16q^{69} - 64q^{70} - 32q^{71} - 8q^{74} + 24q^{75} - 32q^{76} - 32q^{79} - 32q^{80} + 68q^{81} - 8q^{85} - 16q^{86} - 16q^{89} + 12q^{90} + 8q^{91} + 8q^{94} - 16q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1005, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
1005.2.c.a $$2$$ $$8.025$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+iq^{2}+iq^{3}+q^{4}+(2+i)q^{5}-q^{6}+\cdots$$
1005.2.c.b $$4$$ $$8.025$$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(-\beta _{1}-\beta _{3})q^{2}+\beta _{2}q^{3}-4q^{4}+(-1+\cdots)q^{5}+\cdots$$
1005.2.c.c $$28$$ $$8.025$$ None $$0$$ $$0$$ $$0$$ $$0$$
1005.2.c.d $$34$$ $$8.025$$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1005, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1005, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(335, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ ($$1 - 3 T^{2} + 4 T^{4}$$)($$( 1 + 2 T^{2} + 4 T^{4} )^{2}$$)
$3$ ($$1 + T^{2}$$)($$( 1 + T^{2} )^{2}$$)
$5$ ($$1 - 4 T + 5 T^{2}$$)($$1 + 4 T + 8 T^{2} + 20 T^{3} + 25 T^{4}$$)
$7$ ($$( 1 - 7 T^{2} )^{2}$$)($$( 1 - 8 T^{2} + 49 T^{4} )^{2}$$)
$11$ ($$( 1 + 4 T + 11 T^{2} )^{2}$$)($$( 1 + 2 T + 11 T^{2} )^{4}$$)
$13$ ($$( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} )$$)($$( 1 - 20 T^{2} + 169 T^{4} )^{2}$$)
$17$ ($$1 + 2 T^{2} + 289 T^{4}$$)($$1 - 54 T^{2} + 1283 T^{4} - 15606 T^{6} + 83521 T^{8}$$)
$19$ ($$( 1 + 8 T + 19 T^{2} )^{2}$$)($$( 1 + T + 19 T^{2} )^{4}$$)
$23$ ($$1 - 42 T^{2} + 529 T^{4}$$)($$1 - 62 T^{2} + 1803 T^{4} - 32798 T^{6} + 279841 T^{8}$$)
$29$ ($$( 1 - 6 T + 29 T^{2} )^{2}$$)($$( 1 + 10 T + 77 T^{2} + 290 T^{3} + 841 T^{4} )^{2}$$)
$31$ ($$( 1 + 2 T + 31 T^{2} )^{2}$$)($$( 1 + 8 T + 54 T^{2} + 248 T^{3} + 961 T^{4} )^{2}$$)
$37$ ($$( 1 - 37 T^{2} )^{2}$$)($$1 - 82 T^{2} + 3555 T^{4} - 112258 T^{6} + 1874161 T^{8}$$)
$41$ ($$( 1 - 12 T + 41 T^{2} )^{2}$$)($$( 1 + 12 T + 112 T^{2} + 492 T^{3} + 1681 T^{4} )^{2}$$)
$43$ ($$1 + 58 T^{2} + 1849 T^{4}$$)($$( 1 - 50 T^{2} + 1849 T^{4} )^{2}$$)
$47$ ($$1 - 90 T^{2} + 2209 T^{4}$$)($$1 - 78 T^{2} + 4763 T^{4} - 172302 T^{6} + 4879681 T^{8}$$)
$53$ ($$1 - 6 T^{2} + 2809 T^{4}$$)($$( 1 - 52 T^{2} + 2809 T^{4} )^{2}$$)
$59$ ($$( 1 - 12 T + 59 T^{2} )^{2}$$)($$( 1 + 6 T + 121 T^{2} + 354 T^{3} + 3481 T^{4} )^{2}$$)
$61$ ($$( 1 + 2 T + 61 T^{2} )^{2}$$)($$( 1 - 4 T + 72 T^{2} - 244 T^{3} + 3721 T^{4} )^{2}$$)
$67$ ($$1 + T^{2}$$)($$( 1 + T^{2} )^{2}$$)
$71$ ($$( 1 - 8 T + 71 T^{2} )^{2}$$)($$( 1 + 118 T^{2} + 5041 T^{4} )^{2}$$)
$73$ ($$1 - 82 T^{2} + 5329 T^{4}$$)($$1 - 146 T^{2} + 11283 T^{4} - 778034 T^{6} + 28398241 T^{8}$$)
$79$ ($$( 1 + 2 T + 79 T^{2} )^{2}$$)($$( 1 + 8 T + 150 T^{2} + 632 T^{3} + 6241 T^{4} )^{2}$$)
$83$ ($$1 + 30 T^{2} + 6889 T^{4}$$)($$1 - 68 T^{2} + 1110 T^{4} - 468452 T^{6} + 47458321 T^{8}$$)
$89$ ($$( 1 + 14 T + 89 T^{2} )^{2}$$)($$( 1 + 10 T + 197 T^{2} + 890 T^{3} + 7921 T^{4} )^{2}$$)
$97$ ($$1 - 190 T^{2} + 9409 T^{4}$$)($$1 + 136 T^{2} + 17298 T^{4} + 1279624 T^{6} + 88529281 T^{8}$$)