# Properties

 Label 108.3.c Level 108 Weight 3 Character orbit c Rep. character $$\chi_{108}(53,\cdot)$$ Character field $$\Q$$ Dimension 3 Newform subspaces 2 Sturm bound 54 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$108 = 2^{2} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 108.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$54$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(108, [\chi])$$.

Total New Old
Modular forms 45 3 42
Cusp forms 27 3 24
Eisenstein series 18 0 18

## Trace form

 $$3q - 3q^{7} + O(q^{10})$$ $$3q - 3q^{7} + 51q^{13} - 21q^{19} - 87q^{25} + 24q^{31} + 15q^{37} - 66q^{43} + 72q^{49} - 162q^{55} + 87q^{61} + 15q^{67} + 321q^{73} + 231q^{79} - 324q^{85} + 57q^{91} - 147q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(108, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
108.3.c.a $$1$$ $$2.943$$ $$\Q$$ $$\Q(\sqrt{-3})$$ $$0$$ $$0$$ $$0$$ $$11$$ $$q+11q^{7}+23q^{13}-37q^{19}+5^{2}q^{25}+\cdots$$
108.3.c.b $$2$$ $$2.943$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$-14$$ $$q+iq^{5}-7q^{7}+iq^{11}+14q^{13}+2iq^{17}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(108, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(108, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(18, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(27, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(54, [\chi])$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ ($$( 1 - 5 T )( 1 + 5 T )$$)($$1 + 31 T^{2} + 625 T^{4}$$)
$7$ ($$1 - 11 T + 49 T^{2}$$)($$( 1 + 7 T + 49 T^{2} )^{2}$$)
$11$ ($$( 1 - 11 T )( 1 + 11 T )$$)($$1 - 161 T^{2} + 14641 T^{4}$$)
$13$ ($$1 - 23 T + 169 T^{2}$$)($$( 1 - 14 T + 169 T^{2} )^{2}$$)
$17$ ($$( 1 - 17 T )( 1 + 17 T )$$)($$1 - 254 T^{2} + 83521 T^{4}$$)
$19$ ($$1 + 37 T + 361 T^{2}$$)($$( 1 - 8 T + 361 T^{2} )^{2}$$)
$23$ ($$( 1 - 23 T )( 1 + 23 T )$$)($$1 + 238 T^{2} + 279841 T^{4}$$)
$29$ ($$( 1 - 29 T )( 1 + 29 T )$$)($$1 - 1358 T^{2} + 707281 T^{4}$$)
$31$ ($$1 + 46 T + 961 T^{2}$$)($$( 1 - 35 T + 961 T^{2} )^{2}$$)
$37$ ($$1 + 73 T + 1369 T^{2}$$)($$( 1 - 44 T + 1369 T^{2} )^{2}$$)
$41$ ($$( 1 - 41 T )( 1 + 41 T )$$)($$1 - 2066 T^{2} + 2825761 T^{4}$$)
$43$ ($$1 + 22 T + 1849 T^{2}$$)($$( 1 + 22 T + 1849 T^{2} )^{2}$$)
$47$ ($$( 1 - 47 T )( 1 + 47 T )$$)($$1 - 1502 T^{2} + 4879681 T^{4}$$)
$53$ ($$( 1 - 53 T )( 1 + 53 T )$$)($$1 - 5537 T^{2} + 7890481 T^{4}$$)
$59$ ($$( 1 - 59 T )( 1 + 59 T )$$)($$1 - 6638 T^{2} + 12117361 T^{4}$$)
$61$ ($$1 - 47 T + 3721 T^{2}$$)($$( 1 - 20 T + 3721 T^{2} )^{2}$$)
$67$ ($$1 + 13 T + 4489 T^{2}$$)($$( 1 - 14 T + 4489 T^{2} )^{2}$$)
$71$ ($$( 1 - 71 T )( 1 + 71 T )$$)($$1 + 5794 T^{2} + 25411681 T^{4}$$)
$73$ ($$1 - 143 T + 5329 T^{2}$$)($$( 1 - 89 T + 5329 T^{2} )^{2}$$)
$79$ ($$1 - 11 T + 6241 T^{2}$$)($$( 1 - 110 T + 6241 T^{2} )^{2}$$)
$83$ ($$( 1 - 83 T )( 1 + 83 T )$$)($$1 - 13049 T^{2} + 47458321 T^{4}$$)
$89$ ($$( 1 - 89 T )( 1 + 89 T )$$)($$1 - 15518 T^{2} + 62742241 T^{4}$$)
$97$ ($$1 + 169 T + 9409 T^{2}$$)($$( 1 - 11 T + 9409 T^{2} )^{2}$$)