# Properties

 Label 99.2.d Level 99 Weight 2 Character orbit d Rep. character $$\chi_{99}(98,\cdot)$$ Character field $$\Q$$ Dimension 4 Newform subspaces 1 Sturm bound 24 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$99 = 3^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 99.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$33$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$24$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(99, [\chi])$$.

Total New Old
Modular forms 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

## Trace form

 $$4q + 4q^{4} + O(q^{10})$$ $$4q + 4q^{4} - 20q^{16} - 12q^{22} + 12q^{25} - 16q^{31} + 32q^{37} + 4q^{49} - 16q^{55} + 48q^{58} + 4q^{64} - 16q^{67} + 24q^{70} - 48q^{82} + 12q^{88} - 48q^{91} - 40q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(99, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
99.2.d.a $$4$$ $$0.791$$ $$\Q(\sqrt{-2}, \sqrt{3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+q^{4}-\beta _{1}q^{5}-\beta _{3}q^{7}+\beta _{2}q^{8}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(99, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(99, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(33, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$( 1 + T^{2} + 4 T^{4} )^{2}$$
$3$ 1
$5$ $$( 1 - 8 T^{2} + 25 T^{4} )^{2}$$
$7$ $$( 1 - 8 T^{2} + 49 T^{4} )^{2}$$
$11$ $$1 + 10 T^{2} + 121 T^{4}$$
$13$ $$( 1 - 2 T^{2} + 169 T^{4} )^{2}$$
$17$ $$( 1 + 17 T^{2} )^{4}$$
$19$ $$( 1 + 16 T^{2} + 361 T^{4} )^{2}$$
$23$ $$( 1 - 38 T^{2} + 529 T^{4} )^{2}$$
$29$ $$( 1 + 10 T^{2} + 841 T^{4} )^{2}$$
$31$ $$( 1 + 4 T + 31 T^{2} )^{4}$$
$37$ $$( 1 - 8 T + 37 T^{2} )^{4}$$
$41$ $$( 1 + 34 T^{2} + 1681 T^{4} )^{2}$$
$43$ $$( 1 - 80 T^{2} + 1849 T^{4} )^{2}$$
$47$ $$( 1 - 86 T^{2} + 2209 T^{4} )^{2}$$
$53$ $$( 1 - 8 T^{2} + 2809 T^{4} )^{2}$$
$59$ $$( 1 + 10 T^{2} + 3481 T^{4} )^{2}$$
$61$ $$( 1 - 98 T^{2} + 3721 T^{4} )^{2}$$
$67$ $$( 1 + 4 T + 67 T^{2} )^{4}$$
$71$ $$( 1 - 134 T^{2} + 5041 T^{4} )^{2}$$
$73$ $$( 1 - 73 T^{2} )^{4}$$
$79$ $$( 1 - 8 T^{2} + 6241 T^{4} )^{2}$$
$83$ $$( 1 - 26 T^{2} + 6889 T^{4} )^{2}$$
$89$ $$( 1 - 128 T^{2} + 7921 T^{4} )^{2}$$
$97$ $$( 1 + 10 T + 97 T^{2} )^{4}$$