Space of modular forms of level 546, weight 2, and trivial character

• Label: 546.2.a
• Level: $546$
• Weight: $2$
• Character orbit: 546.a
• Rep. character: $\chi_{546}(1,\cdot)$
• Character field: $\Q$
• Dimension: $13$
• Newform subspaces: $10$
• Sturm bound: $224$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(224\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(546))\).

	Total	New	Old
Modular forms	120	13	107
Cusp forms	105	13	92
Eisenstein series	15	0	15

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	\(7\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(1\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(2\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(1\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(1\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(1\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(2\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(2\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(2\)
Plus space				\(+\)	\(1\)
Minus space				\(-\)	\(12\)

Trace form

\( 13 q + q^{2} + q^{3} + 13 q^{4} + 6 q^{5} + q^{6} + q^{7} + q^{8} + 13 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(546))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	7	13
546.2.a.a	$546$	$2$	546.a	1.a	$1$	$1$	$1$	$4.360$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(-1\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
546.2.a.b	$546$	$2$	546.a	1.a	$1$	$1$	$1$	$4.360$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(1\)	\(-2\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
546.2.a.c	$546$	$2$	546.a	1.a	$1$	$1$	$1$	$4.360$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(1\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
546.2.a.d	$546$	$2$	546.a	1.a	$1$	$1$	$1$	$4.360$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(3\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+q^{7}+\cdots\)
546.2.a.e	$546$	$2$	546.a	1.a	$1$	$1$	$1$	$4.360$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(-1\)	\(3\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}-q^{7}+\cdots\)
546.2.a.f	$546$	$2$	546.a	1.a	$1$	$1$	$1$	$4.360$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
546.2.a.g	$546$	$2$	546.a	1.a	$1$	$1$	$1$	$4.360$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(1\)	\(2\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)
546.2.a.h	$546$	$2$	546.a	1.a	$1$	$2$	$2$	$4.360$	\(\Q(\sqrt{57}) \)	None	✓	$1$	$0$	\(-2\)	\(-2\)	\(-1\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-\beta q^{5}+q^{6}+q^{7}+\cdots\)
546.2.a.i	$546$	$2$	546.a	1.a	$1$	$2$	$2$	$4.360$	\(\Q(\sqrt{41}) \)	None	✓	$1$	$0$	\(2\)	\(-2\)	\(-1\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-\beta q^{5}-q^{6}+q^{7}+\cdots\)
546.2.a.j	$546$	$2$	546.a	1.a	$1$	$2$	$2$	$4.360$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(2\)	\(2\)	\(3\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+(2-\beta )q^{5}+q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(546))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(546)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 2}\)