# Properties

 Label 4027.2.a Level 4027 Weight 2 Character orbit a Rep. character $$\chi_{4027}(1,\cdot)$$ Character field $$\Q$$ Dimension 335 Newform subspaces 3 Sturm bound 671 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ = $$4027$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 4027.a (trivial) Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$671$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(4027))$$.

Total New Old
Modular forms 336 336 0
Cusp forms 335 335 0
Eisenstein series 1 1 0

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators.

$$4027$$Dim.
$$+$$$$159$$
$$-$$$$176$$

## Trace form

 $$335q - 2q^{2} - 4q^{3} + 334q^{4} - 6q^{6} - 2q^{7} - 12q^{8} + 329q^{9} + O(q^{10})$$ $$335q - 2q^{2} - 4q^{3} + 334q^{4} - 6q^{6} - 2q^{7} - 12q^{8} + 329q^{9} - 2q^{10} - 28q^{12} - 2q^{13} - 4q^{14} - 4q^{15} + 328q^{16} + 4q^{17} - 4q^{18} - 2q^{19} + 8q^{20} - 10q^{21} - 8q^{22} + 6q^{23} - 28q^{24} + 341q^{25} + 8q^{26} - 28q^{27} - 10q^{28} + 4q^{29} - 14q^{30} - 10q^{31} - 26q^{32} + 10q^{33} + 18q^{34} - 6q^{35} + 284q^{36} + 2q^{37} + 8q^{38} - 4q^{39} + 10q^{40} + 16q^{41} - 60q^{42} - 30q^{43} - 8q^{44} - 2q^{45} - 26q^{46} - 12q^{47} - 94q^{48} + 341q^{49} - 22q^{50} - 22q^{51} - 52q^{52} + 2q^{53} - 72q^{54} + 2q^{55} - 36q^{56} - 4q^{57} - 4q^{58} + 2q^{59} - 60q^{60} + 6q^{61} + 24q^{62} - 14q^{63} + 308q^{64} + 50q^{65} - 24q^{66} - 54q^{67} + 16q^{68} + 18q^{69} - 40q^{70} + 32q^{71} - 48q^{72} + 2q^{73} - 26q^{74} - 52q^{75} - 10q^{76} + 46q^{77} - 6q^{79} + 18q^{80} + 303q^{81} - 30q^{82} + 32q^{83} - 46q^{84} + 60q^{85} - 36q^{86} - 12q^{87} - 72q^{88} + 18q^{89} + 10q^{90} - 40q^{91} - 12q^{92} + 14q^{93} + 26q^{94} - 32q^{95} - 64q^{96} + 14q^{97} + 14q^{98} - 14q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(4027))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 4027
4027.2.a.a $$2$$ $$32.156$$ $$\Q(\sqrt{5})$$ None $$-1$$ $$-2$$ $$-2$$ $$-7$$ $$-$$ $$q-\beta q^{2}+(-2+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots$$
4027.2.a.b $$159$$ $$32.156$$ None $$-22$$ $$-19$$ $$-70$$ $$-19$$ $$+$$
4027.2.a.c $$174$$ $$32.156$$ None $$21$$ $$17$$ $$72$$ $$24$$ $$-$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ ($$1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4}$$)
$3$ ($$1 + 2 T + 2 T^{2} + 6 T^{3} + 9 T^{4}$$)
$5$ ($$( 1 + T + 5 T^{2} )^{2}$$)
$7$ ($$1 + 7 T + 25 T^{2} + 49 T^{3} + 49 T^{4}$$)
$11$ ($$( 1 + T + 11 T^{2} )^{2}$$)
$13$ ($$1 + 3 T + 27 T^{2} + 39 T^{3} + 169 T^{4}$$)
$17$ ($$1 - T + 3 T^{2} - 17 T^{3} + 289 T^{4}$$)
$19$ ($$( 1 + 5 T + 19 T^{2} )^{2}$$)
$23$ ($$1 + 11 T + 75 T^{2} + 253 T^{3} + 529 T^{4}$$)
$29$ ($$1 + 9 T + 77 T^{2} + 261 T^{3} + 841 T^{4}$$)
$31$ ($$1 + 12 T + 93 T^{2} + 372 T^{3} + 961 T^{4}$$)
$37$ ($$1 + 4 T - 2 T^{2} + 148 T^{3} + 1369 T^{4}$$)
$41$ ($$1 + 10 T + 102 T^{2} + 410 T^{3} + 1681 T^{4}$$)
$43$ ($$1 - 4 T + 45 T^{2} - 172 T^{3} + 1849 T^{4}$$)
$47$ ($$1 + 8 T + 90 T^{2} + 376 T^{3} + 2209 T^{4}$$)
$53$ ($$1 - 8 T + 117 T^{2} - 424 T^{3} + 2809 T^{4}$$)
$59$ ($$1 + 4 T + 77 T^{2} + 236 T^{3} + 3481 T^{4}$$)
$61$ ($$1 - 3 T^{2} + 3721 T^{4}$$)
$67$ ($$1 - 2 T + 90 T^{2} - 134 T^{3} + 4489 T^{4}$$)
$71$ ($$1 + 15 T + 187 T^{2} + 1065 T^{3} + 5041 T^{4}$$)
$73$ ($$1 + 11 T + 145 T^{2} + 803 T^{3} + 5329 T^{4}$$)
$79$ ($$( 1 - 13 T + 79 T^{2} )^{2}$$)
$83$ ($$1 + 13 T + 107 T^{2} + 1079 T^{3} + 6889 T^{4}$$)
$89$ ($$1 + 15 T + 223 T^{2} + 1335 T^{3} + 7921 T^{4}$$)
$97$ ($$1 - 18 T + 255 T^{2} - 1746 T^{3} + 9409 T^{4}$$)