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 + 6 * q^10 + 12 * q^11 + q^12 + q^13 + q^14 + 6 * q^15 + 13 * q^16 + 2 * q^17 + q^18 + 4 * q^19 + 6 * q^20 - 3 * q^21 + 4 * q^22 + q^24 + 27 * q^25 + q^26 + q^27 + q^28 + 6 * q^29 - 2 * q^30 + 16 * q^31 + q^32 - 4 * q^33 + 18 * q^34 - 2 * q^35 + 13 * q^36 - 10 * q^37 + 4 * q^38 + q^39 + 6 * q^40 + 10 * q^41 + q^42 + 4 * q^43 + 12 * q^44 + 6 * q^45 - 16 * q^46 - 16 * q^47 + q^48 + 13 * q^49 - q^50 + 2 * q^51 + q^52 + 14 * q^53 + q^54 + 8 * q^55 + q^56 - 28 * q^57 + 6 * q^58 + 28 * q^59 + 6 * q^60 - 18 * q^61 - 32 * q^62 + q^63 + 13 * q^64 - 2 * q^65 - 4 * q^66 - 4 * q^67 + 2 * q^68 + 8 * q^69 - 10 * q^70 - 8 * q^71 + q^72 - 38 * q^73 + 6 * q^74 - 33 * q^75 + 4 * q^76 + 12 * q^77 - 3 * q^78 + 6 * q^80 + 13 * q^81 - 14 * q^82 - 12 * q^83 - 3 * q^84 - 36 * q^85 - 20 * q^86 - 10 * q^87 + 4 * q^88 - 6 * q^89 + 6 * q^90 - 3 * q^91 - 32 * q^93 - 24 * q^94 - 40 * q^95 + q^96 - 30 * q^97 + q^98 + 12 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	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	✓	✓	✓	✓	546.2.a.a	$1$	$0$	\(-1\)	\(-1\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
546.2.a.b	$546$	$2$	546.a	1.a	$1$	$1$	$1$	$4.360$	\(\Q\)	None	✓	✓	✓	✓	546.2.a.b	$1$	$1$	\(-1\)	\(1\)	\(-2\)	\(-1\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
546.2.a.c	$546$	$2$	546.a	1.a	$1$	$1$	$1$	$4.360$	\(\Q\)	None	✓	✓	✓	✓	546.2.a.c	$1$	$0$	\(-1\)	\(1\)	\(1\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
546.2.a.d	$546$	$2$	546.a	1.a	$1$	$1$	$1$	$4.360$	\(\Q\)	None	✓	✓	✓	✓	546.2.a.d	$1$	$0$	\(-1\)	\(1\)	\(3\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+q^{7}+\cdots\)
546.2.a.e	$546$	$2$	546.a	1.a	$1$	$1$	$1$	$4.360$	\(\Q\)	None	✓	✓	✓	✓	546.2.a.e	$1$	$0$	\(1\)	\(-1\)	\(3\)	\(-1\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}-q^{7}+\cdots\)
546.2.a.f	$546$	$2$	546.a	1.a	$1$	$1$	$1$	$4.360$	\(\Q\)	None	✓	✓			546.2.a.f	$1$	$0$	\(1\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
546.2.a.g	$546$	$2$	546.a	1.a	$1$	$1$	$1$	$4.360$	\(\Q\)	None	✓	✓			546.2.a.g	$1$	$0$	\(1\)	\(1\)	\(2\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)
546.2.a.h	$546$	$2$	546.a	1.a	$1$	$2$	$2$	$4.360$	\(\Q(\sqrt{57}) \)	None	✓	✓	✓	✓	546.2.a.h	$1$	$0$	\(-2\)	\(-2\)	\(-1\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-\beta q^{5}+q^{6}+q^{7}+\cdots\)
546.2.a.i	$546$	$2$	546.a	1.a	$1$	$2$	$2$	$4.360$	\(\Q(\sqrt{41}) \)	None	✓	✓	✓	✓	546.2.a.i	$1$	$0$	\(2\)	\(-2\)	\(-1\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-\beta q^{5}-q^{6}+q^{7}+\cdots\)
546.2.a.j	$546$	$2$	546.a	1.a	$1$	$2$	$2$	$4.360$	\(\Q(\sqrt{17}) \)	None	✓	✓	✓	✓	546.2.a.j	$1$	$0$	\(2\)	\(2\)	\(3\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+(2-\beta )q^{5}+q^{6}+\cdots\)

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

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