LMFDB - Space of Modular Forms of Level 224, Weight 2, and Character 224.f

Defining parameters

Level:	$ N $	=	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	224.f (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	=	$ 28 $
Character field:			$\Q$
Newform subspaces:			$ 1 $
Sturm bound:			$64$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(224, [\chi])$.

	Total	New	Old
Modular forms	40	8	32
Cusp forms	24	8	16
Eisenstein series	16	0	16

Trace form

Decomposition of $S_{2}^{\mathrm{new}}(224, [\chi])$ into newform subspaces

Label	Dim.	$A$	Field	CM	Traces				$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	$q$-expansion
224.2.f.a	$8$	$1.789$	$\Q(\zeta_{16})$	None	$0$	$0$	$0$	$0$	$q-\zeta_{16}^{2}q^{3}-\zeta_{16}^{5}q^{5}-\zeta_{16}^{6}q^{7}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(224, [\chi])$ into lower level spaces

$ S_{2}^{\mathrm{old}}(224, [\chi]) \cong $ $S_{2}^{\mathrm{new}}(28, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(112, [\chi])$$^{\oplus 2}$

Hecke Characteristic Polynomials

$p$	$F_p(T)$
$2$	1
$3$	$ ( 1 + 4 T^{2} + 14 T^{4} + 36 T^{6} + 81 T^{8} )^{2} $
$5$	$ ( 1 - 12 T^{2} + 78 T^{4} - 300 T^{6} + 625 T^{8} )^{2} $
$7$	$ 1 - 4 T^{2} - 26 T^{4} - 196 T^{6} + 2401 T^{8} $
$11$	$ ( 1 - 18 T^{2} + 121 T^{4} )^{4} $
$13$	$ ( 1 - 12 T^{2} + 366 T^{4} - 2028 T^{6} + 28561 T^{8} )^{2} $
$17$	$ ( 1 - 4 T + 6 T^{2} - 68 T^{3} + 289 T^{4} )^{2}( 1 + 4 T + 6 T^{2} + 68 T^{3} + 289 T^{4} )^{2} $
$19$	$ ( 1 + 36 T^{2} + 1038 T^{4} + 12996 T^{6} + 130321 T^{8} )^{2} $
$23$	$ ( 1 - 20 T^{2} + 646 T^{4} - 10580 T^{6} + 279841 T^{8} )^{2} $
$29$	$ ( 1 + 4 T + 30 T^{2} + 116 T^{3} + 841 T^{4} )^{4} $
$31$	$ ( 1 + 60 T^{2} + 2310 T^{4} + 57660 T^{6} + 923521 T^{8} )^{2} $
$37$	$ ( 1 + 4 T + 46 T^{2} + 148 T^{3} + 1369 T^{4} )^{4} $
$41$	$ ( 1 - 4 T^{2} + 3238 T^{4} - 6724 T^{6} + 2825761 T^{8} )^{2} $
$43$	$ ( 1 - 100 T^{2} + 5686 T^{4} - 184900 T^{6} + 3418801 T^{8} )^{2} $
$47$	$ ( 1 + 124 T^{2} + 7750 T^{4} + 273916 T^{6} + 4879681 T^{8} )^{2} $
$53$	$ ( 1 + 2 T + 53 T^{2} )^{8} $
$59$	$ ( 1 + 132 T^{2} + 10926 T^{4} + 459492 T^{6} + 12117361 T^{8} )^{2} $
$61$	$ ( 1 - 236 T^{2} + 21358 T^{4} - 878156 T^{6} + 13845841 T^{8} )^{2} $
$67$	$ ( 1 - 4 T^{2} - 3818 T^{4} - 17956 T^{6} + 20151121 T^{8} )^{2} $
$71$	$ ( 1 - 196 T^{2} + 18534 T^{4} - 988036 T^{6} + 25411681 T^{8} )^{2} $
$73$	$ ( 1 - 132 T^{2} + 8742 T^{4} - 703428 T^{6} + 28398241 T^{8} )^{2} $
$79$	$ ( 1 - 100 T^{2} + 11782 T^{4} - 624100 T^{6} + 38950081 T^{8} )^{2} $
$83$	$ ( 1 + 196 T^{2} + 19150 T^{4} + 1350244 T^{6} + 47458321 T^{8} )^{2} $
$89$	$ ( 1 - 324 T^{2} + 41958 T^{4} - 2566404 T^{6} + 62742241 T^{8} )^{2} $
$97$	$ ( 1 - 68 T^{2} + 19462 T^{4} - 639812 T^{6} + 88529281 T^{8} )^{2} $
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Introduction	Features
Universe	News

Level:	\( N \)	=	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	224.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	=	\( 28 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(64\)
Trace bound:			\(0\)

Label	Dim.	\(A\)	Field	CM	Traces				$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	$q$-expansion
224.2.f.a	\(8\)	\(1.789\)	\(\Q(\zeta_{16})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q-\zeta_{16}^{2}q^{3}-\zeta_{16}^{5}q^{5}-\zeta_{16}^{6}q^{7}+\cdots\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(224, [\chi])\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(224, [\chi])\) into lower level spaces

Hecke Characteristic Polynomials

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	224.2.f

Level	224
Weight	2
Character orbit	f
Rep. character	\(\chi_{224}(223,\cdot)\)
Character field	\(\Q\)
Dimension	8
Newform subspaces	1
Sturm bound	64
Trace bound	0

$p$	$F_p(T)$
$2$	1
$3$	\( ( 1 + 4 T^{2} + 14 T^{4} + 36 T^{6} + 81 T^{8} )^{2} \)
$5$	\( ( 1 - 12 T^{2} + 78 T^{4} - 300 T^{6} + 625 T^{8} )^{2} \)
$7$	\( 1 - 4 T^{2} - 26 T^{4} - 196 T^{6} + 2401 T^{8} \)
$11$	\( ( 1 - 18 T^{2} + 121 T^{4} )^{4} \)
$13$	\( ( 1 - 12 T^{2} + 366 T^{4} - 2028 T^{6} + 28561 T^{8} )^{2} \)
$17$	\( ( 1 - 4 T + 6 T^{2} - 68 T^{3} + 289 T^{4} )^{2}( 1 + 4 T + 6 T^{2} + 68 T^{3} + 289 T^{4} )^{2} \)
$19$	\( ( 1 + 36 T^{2} + 1038 T^{4} + 12996 T^{6} + 130321 T^{8} )^{2} \)
$23$	\( ( 1 - 20 T^{2} + 646 T^{4} - 10580 T^{6} + 279841 T^{8} )^{2} \)
$29$	\( ( 1 + 4 T + 30 T^{2} + 116 T^{3} + 841 T^{4} )^{4} \)
$31$	\( ( 1 + 60 T^{2} + 2310 T^{4} + 57660 T^{6} + 923521 T^{8} )^{2} \)
$37$	\( ( 1 + 4 T + 46 T^{2} + 148 T^{3} + 1369 T^{4} )^{4} \)
$41$	\( ( 1 - 4 T^{2} + 3238 T^{4} - 6724 T^{6} + 2825761 T^{8} )^{2} \)
$43$	\( ( 1 - 100 T^{2} + 5686 T^{4} - 184900 T^{6} + 3418801 T^{8} )^{2} \)
$47$	\( ( 1 + 124 T^{2} + 7750 T^{4} + 273916 T^{6} + 4879681 T^{8} )^{2} \)
$53$	\( ( 1 + 2 T + 53 T^{2} )^{8} \)
$59$	\( ( 1 + 132 T^{2} + 10926 T^{4} + 459492 T^{6} + 12117361 T^{8} )^{2} \)
$61$	\( ( 1 - 236 T^{2} + 21358 T^{4} - 878156 T^{6} + 13845841 T^{8} )^{2} \)
$67$	\( ( 1 - 4 T^{2} - 3818 T^{4} - 17956 T^{6} + 20151121 T^{8} )^{2} \)
$71$	\( ( 1 - 196 T^{2} + 18534 T^{4} - 988036 T^{6} + 25411681 T^{8} )^{2} \)
$73$	\( ( 1 - 132 T^{2} + 8742 T^{4} - 703428 T^{6} + 28398241 T^{8} )^{2} \)
$79$	\( ( 1 - 100 T^{2} + 11782 T^{4} - 624100 T^{6} + 38950081 T^{8} )^{2} \)
$83$	\( ( 1 + 196 T^{2} + 19150 T^{4} + 1350244 T^{6} + 47458321 T^{8} )^{2} \)
$89$	\( ( 1 - 324 T^{2} + 41958 T^{4} - 2566404 T^{6} + 62742241 T^{8} )^{2} \)
$97$	\( ( 1 - 68 T^{2} + 19462 T^{4} - 639812 T^{6} + 88529281 T^{8} )^{2} \)
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