LMFDB - Space of Modular Forms of Level 276, Weight 1, and Character 276.h

Defining parameters

Level:	$ N $	=	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	=	$ 1 $
Character orbit:	$[\chi]$	=	276.h (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	=	$ 276 $
Character field:			$\Q$
Newform subspaces:			$ 4 $
Sturm bound:			$48$
Trace bound:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{1}(276, [\chi])$.

	Total	New
Modular forms	10	10
Cusp forms	6	6
Eisenstein series	4	4

The following table gives the dimensions of subspaces with specified projective image type.

	$D_n$	$A_4$	$S_4$	$A_5$
Dimension	6	0	0	0

Trace form

Decomposition of $S_{1}^{\mathrm{new}}(276, [\chi])$ into newform subspaces

Label	Dim.	$A$	Field	Image	CM	RM	Traces				$q$-expansion
Label	Dim.	$A$	Field	Image	CM	RM	$a_2$	$a_3$	$a_5$	$a_7$	$q$-expansion
276.1.h.a	$1$	$0.138$	$\Q$	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-69}) $	$\Q(\sqrt{3}) $	$-1$	$1$	$0$	$0$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
276.1.h.b	$1$	$0.138$	$\Q$	$D_{2}$	$\Q(\sqrt{-23}) $, $\Q(\sqrt{-69}) $	$\Q(\sqrt{3}) $	$1$	$-1$	$0$	$0$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
276.1.h.c	$2$	$0.138$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-23}) $	None	$-1$	$1$	$0$	$0$	$q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots$
276.1.h.d	$2$	$0.138$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-23}) $	None	$1$	$-1$	$0$	$0$	$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-q^{6}-q^{8}+\cdots$

Hecke Characteristic Polynomials

$p$	$F_p(T)$
$2$	($ 1 + T $)($ 1 - T $)($ 1 + T + T^{2} $)($ 1 - T + T^{2} $)
$3$	($ 1 - T $)($ 1 + T $)($ 1 - T + T^{2} $)($ 1 + T + T^{2} $)
$5$	($ 1 + T^{2} $)($ 1 + T^{2} $)($ ( 1 + T^{2} )^{2} $)($ ( 1 + T^{2} )^{2} $)
$7$	($ 1 + T^{2} $)($ 1 + T^{2} $)($ ( 1 + T^{2} )^{2} $)($ ( 1 + T^{2} )^{2} $)
$11$	($ ( 1 - T )( 1 + T ) $)($ ( 1 - T )( 1 + T ) $)($ ( 1 - T )^{2}( 1 + T )^{2} $)($ ( 1 - T )^{2}( 1 + T )^{2} $)
$13$	($ ( 1 + T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 - T + T^{2} )^{2} $)($ ( 1 - T + T^{2} )^{2} $)
$17$	($ 1 + T^{2} $)($ 1 + T^{2} $)($ ( 1 + T^{2} )^{2} $)($ ( 1 + T^{2} )^{2} $)
$19$	($ 1 + T^{2} $)($ 1 + T^{2} $)($ ( 1 + T^{2} )^{2} $)($ ( 1 + T^{2} )^{2} $)
$23$	($ 1 - T $)($ 1 + T $)($ ( 1 + T )^{2} $)($ ( 1 - T )^{2} $)
$29$	($ ( 1 - T )( 1 + T ) $)($ ( 1 - T )( 1 + T ) $)($ ( 1 - T + T^{2} )( 1 + T + T^{2} ) $)($ ( 1 - T + T^{2} )( 1 + T + T^{2} ) $)
$31$	($ ( 1 - T )( 1 + T ) $)($ ( 1 - T )( 1 + T ) $)($ ( 1 - T + T^{2} )( 1 + T + T^{2} ) $)($ ( 1 - T + T^{2} )( 1 + T + T^{2} ) $)
$37$	($ ( 1 - T )( 1 + T ) $)($ ( 1 - T )( 1 + T ) $)($ ( 1 - T )^{2}( 1 + T )^{2} $)($ ( 1 - T )^{2}( 1 + T )^{2} $)
$41$	($ ( 1 - T )( 1 + T ) $)($ ( 1 - T )( 1 + T ) $)($ ( 1 - T + T^{2} )( 1 + T + T^{2} ) $)($ ( 1 - T + T^{2} )( 1 + T + T^{2} ) $)
$43$	($ 1 + T^{2} $)($ 1 + T^{2} $)($ ( 1 + T^{2} )^{2} $)($ ( 1 + T^{2} )^{2} $)
$47$	($ ( 1 + T )^{2} $)($ ( 1 - T )^{2} $)($ ( 1 + T + T^{2} )^{2} $)($ ( 1 - T + T^{2} )^{2} $)
$53$	($ 1 + T^{2} $)($ 1 + T^{2} $)($ ( 1 + T^{2} )^{2} $)($ ( 1 + T^{2} )^{2} $)
$59$	($ ( 1 + T )^{2} $)($ ( 1 - T )^{2} $)($ ( 1 - T )^{4} $)($ ( 1 + T )^{4} $)
$61$	($ ( 1 - T )( 1 + T ) $)($ ( 1 - T )( 1 + T ) $)($ ( 1 - T )^{2}( 1 + T )^{2} $)($ ( 1 - T )^{2}( 1 + T )^{2} $)
$67$	($ 1 + T^{2} $)($ 1 + T^{2} $)($ ( 1 + T^{2} )^{2} $)($ ( 1 + T^{2} )^{2} $)
$71$	($ ( 1 - T )^{2} $)($ ( 1 + T )^{2} $)($ ( 1 - T + T^{2} )^{2} $)($ ( 1 + T + T^{2} )^{2} $)
$73$	($ ( 1 - T )^{2} $)($ ( 1 - T )^{2} $)($ ( 1 + T + T^{2} )^{2} $)($ ( 1 + T + T^{2} )^{2} $)
$79$	($ 1 + T^{2} $)($ 1 + T^{2} $)($ ( 1 + T^{2} )^{2} $)($ ( 1 + T^{2} )^{2} $)
$83$	($ ( 1 - T )( 1 + T ) $)($ ( 1 - T )( 1 + T ) $)($ ( 1 - T )^{2}( 1 + T )^{2} $)($ ( 1 - T )^{2}( 1 + T )^{2} $)
$89$	($ 1 + T^{2} $)($ 1 + T^{2} $)($ ( 1 + T^{2} )^{2} $)($ ( 1 + T^{2} )^{2} $)
$97$	($ ( 1 - T )( 1 + T ) $)($ ( 1 - T )( 1 + T ) $)($ ( 1 - T )^{2}( 1 + T )^{2} $)($ ( 1 - T )^{2}( 1 + T )^{2} $)
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Introduction	Features
Universe	News

Level:	\( N \)	=	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	=	\( 1 \)
Character orbit:	\([\chi]\)	=	276.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	=	\( 276 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(48\)
Trace bound:			\(2\)

Label	Dim.	\(A\)	Field	Image	CM	RM	Traces				$q$-expansion
Label	Dim.	\(A\)	Field	Image	CM	RM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	$q$-expansion
276.1.h.a	\(1\)	\(0.138\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-69}) \)	\(\Q(\sqrt{3}) \)	\(-1\)	\(1\)	\(0\)	\(0\)	\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
276.1.h.b	\(1\)	\(0.138\)	\(\Q\)	\(D_{2}\)	\(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-69}) \)	\(\Q(\sqrt{3}) \)	\(1\)	\(-1\)	\(0\)	\(0\)	\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
276.1.h.c	\(2\)	\(0.138\)	\(\Q(\sqrt{-3}) \)	\(D_{6}\)	\(\Q(\sqrt{-23}) \)	None	\(-1\)	\(1\)	\(0\)	\(0\)	\(q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\)
276.1.h.d	\(2\)	\(0.138\)	\(\Q(\sqrt{-3}) \)	\(D_{6}\)	\(\Q(\sqrt{-23}) \)	None	\(1\)	\(-1\)	\(0\)	\(0\)	\(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-q^{6}-q^{8}+\cdots\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{1}^{\mathrm{new}}(276, [\chi])\) into newform subspaces

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	276.1.h

Level	276
Weight	1
Character orbit	h
Rep. character	\(\chi_{276}(275,\cdot)\)
Character field	\(\Q\)
Dimension	6
Newform subspaces	4
Sturm bound	48
Trace bound	2

$p$	$F_p(T)$
$2$	(\( 1 + T \))(\( 1 - T \))(\( 1 + T + T^{2} \))(\( 1 - T + T^{2} \))
$3$	(\( 1 - T \))(\( 1 + T \))(\( 1 - T + T^{2} \))(\( 1 + T + T^{2} \))
$5$	(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))
$7$	(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))
$11$	(\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))
$13$	(\( ( 1 + T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))
$17$	(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))
$19$	(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))
$23$	(\( 1 - T \))(\( 1 + T \))(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))
$29$	(\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))
$31$	(\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))
$37$	(\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))
$41$	(\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))(\( ( 1 - T + T^{2} )( 1 + T + T^{2} ) \))
$43$	(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))
$47$	(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))
$53$	(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))
$59$	(\( ( 1 + T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{4} \))(\( ( 1 + T )^{4} \))
$61$	(\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))
$67$	(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))
$71$	(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))
$73$	(\( ( 1 - T )^{2} \))(\( ( 1 - T )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))
$79$	(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))
$83$	(\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))
$89$	(\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))
$97$	(\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )( 1 + T ) \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))
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