# Properties

 Label 189.2.c Level 189 Weight 2 Character orbit c Rep. character $$\chi_{189}(188,\cdot)$$ Character field $$\Q$$ Dimension 10 Newform subspaces 3 Sturm bound 48 Trace bound 4

# Related objects

## Defining parameters

 Level: $$N$$ = $$189 = 3^{3} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 189.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$21$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$48$$ Trace bound: $$4$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(189, [\chi])$$.

Total New Old
Modular forms 30 10 20
Cusp forms 18 10 8
Eisenstein series 12 0 12

## Trace form

 $$10q - 8q^{4} - 3q^{7} + O(q^{10})$$ $$10q - 8q^{4} - 3q^{7} - 12q^{16} - 28q^{22} + 22q^{25} + 26q^{28} - 6q^{37} + 12q^{43} - 4q^{46} - 29q^{49} + 80q^{58} + 36q^{64} - 22q^{67} - 36q^{70} - 10q^{79} - 36q^{85} + 4q^{88} + 27q^{91} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(189, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
189.2.c.a $$2$$ $$1.509$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$1$$ $$q+2q^{4}+\zeta_{6}q^{7}+(1-2\zeta_{6})q^{13}+4q^{16}+\cdots$$
189.2.c.b $$4$$ $$1.509$$ $$\Q(\sqrt{-3}, \sqrt{-5})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q-\beta _{1}q^{2}-3q^{4}-\beta _{3}q^{5}+(-2+\beta _{2}+\cdots)q^{7}+\cdots$$
189.2.c.c $$4$$ $$1.509$$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q-\beta _{1}q^{2}-\beta _{2}q^{5}+(1-\beta _{3})q^{7}-2\beta _{1}q^{8}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(189, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(189, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ ($$( 1 - 2 T^{2} )^{2}$$)($$( 1 + T^{2} + 4 T^{4} )^{2}$$)($$( 1 - 2 T^{2} + 4 T^{4} )^{2}$$)
$3$ 1
$5$ ($$( 1 + 5 T^{2} )^{2}$$)($$( 1 - 5 T^{2} + 25 T^{4} )^{2}$$)($$( 1 + 7 T^{2} + 25 T^{4} )^{2}$$)
$7$ ($$1 - T + 7 T^{2}$$)($$( 1 + 4 T + 7 T^{2} )^{2}$$)($$( 1 - 2 T + 7 T^{2} )^{2}$$)
$11$ ($$( 1 - 11 T^{2} )^{2}$$)($$( 1 - 17 T^{2} + 121 T^{4} )^{2}$$)($$( 1 - 20 T^{2} + 121 T^{4} )^{2}$$)
$13$ ($$( 1 - 5 T + 13 T^{2} )( 1 + 5 T + 13 T^{2} )$$)($$( 1 - 14 T^{2} + 169 T^{4} )^{2}$$)($$( 1 - 20 T^{2} + 169 T^{4} )^{2}$$)
$17$ ($$( 1 + 17 T^{2} )^{2}$$)($$( 1 + 17 T^{2} )^{4}$$)($$( 1 + 7 T^{2} + 289 T^{4} )^{2}$$)
$19$ ($$( 1 - 7 T + 19 T^{2} )( 1 + 7 T + 19 T^{2} )$$)($$( 1 - 7 T + 19 T^{2} )^{2}( 1 + 7 T + 19 T^{2} )^{2}$$)($$( 1 + 16 T^{2} + 361 T^{4} )^{2}$$)
$23$ ($$( 1 - 23 T^{2} )^{2}$$)($$( 1 - 41 T^{2} + 529 T^{4} )^{2}$$)($$( 1 - 38 T^{2} + 529 T^{4} )^{2}$$)
$29$ ($$( 1 - 29 T^{2} )^{2}$$)($$( 1 - 38 T^{2} + 841 T^{4} )^{2}$$)($$( 1 - 8 T^{2} + 841 T^{4} )^{2}$$)
$31$ ($$( 1 - 4 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} )$$)($$( 1 - 11 T + 31 T^{2} )^{2}( 1 + 11 T + 31 T^{2} )^{2}$$)($$( 1 - 56 T^{2} + 961 T^{4} )^{2}$$)
$37$ ($$( 1 + 11 T + 37 T^{2} )^{2}$$)($$( 1 + T + 37 T^{2} )^{4}$$)($$( 1 - 5 T + 37 T^{2} )^{4}$$)
$41$ ($$( 1 + 41 T^{2} )^{2}$$)($$( 1 + 67 T^{2} + 1681 T^{4} )^{2}$$)($$( 1 + 7 T^{2} + 1681 T^{4} )^{2}$$)
$43$ ($$( 1 + 8 T + 43 T^{2} )^{2}$$)($$( 1 - 2 T + 43 T^{2} )^{4}$$)($$( 1 - 5 T + 43 T^{2} )^{4}$$)
$47$ ($$( 1 + 47 T^{2} )^{2}$$)($$( 1 + 34 T^{2} + 2209 T^{4} )^{2}$$)($$( 1 + 19 T^{2} + 2209 T^{4} )^{2}$$)
$53$ ($$( 1 - 53 T^{2} )^{2}$$)($$( 1 - 26 T^{2} + 2809 T^{4} )^{2}$$)($$( 1 + 22 T^{2} + 2809 T^{4} )^{2}$$)
$59$ ($$( 1 + 59 T^{2} )^{2}$$)($$( 1 + 58 T^{2} + 3481 T^{4} )^{2}$$)($$( 1 + 43 T^{2} + 3481 T^{4} )^{2}$$)
$61$ ($$( 1 - T + 61 T^{2} )( 1 + T + 61 T^{2} )$$)($$( 1 - 14 T + 61 T^{2} )^{2}( 1 + 14 T + 61 T^{2} )^{2}$$)($$( 1 - 116 T^{2} + 3721 T^{4} )^{2}$$)
$67$ ($$( 1 - 5 T + 67 T^{2} )^{2}$$)($$( 1 + 10 T + 67 T^{2} )^{4}$$)($$( 1 - 2 T + 67 T^{2} )^{4}$$)
$71$ ($$( 1 - 71 T^{2} )^{2}$$)($$( 1 - 17 T^{2} + 5041 T^{4} )^{2}$$)($$( 1 + 58 T^{2} + 5041 T^{4} )^{2}$$)
$73$ ($$( 1 - 7 T + 73 T^{2} )( 1 + 7 T + 73 T^{2} )$$)($$( 1 - 38 T^{2} + 5329 T^{4} )^{2}$$)($$( 1 - 73 T^{2} )^{4}$$)
$79$ ($$( 1 - 17 T + 79 T^{2} )^{2}$$)($$( 1 - 2 T + 79 T^{2} )^{4}$$)($$( 1 + 13 T + 79 T^{2} )^{4}$$)
$83$ ($$( 1 + 83 T^{2} )^{2}$$)($$( 1 + 106 T^{2} + 6889 T^{4} )^{2}$$)($$( 1 + 163 T^{2} + 6889 T^{4} )^{2}$$)
$89$ ($$( 1 + 89 T^{2} )^{2}$$)($$( 1 + 43 T^{2} + 7921 T^{4} )^{2}$$)($$( 1 + 70 T^{2} + 7921 T^{4} )^{2}$$)
$97$ ($$( 1 - 19 T + 97 T^{2} )( 1 + 19 T + 97 T^{2} )$$)($$( 1 - 14 T + 97 T^{2} )^{2}( 1 + 14 T + 97 T^{2} )^{2}$$)($$( 1 + 100 T^{2} + 9409 T^{4} )^{2}$$)