Space of modular forms of level 273, weight 2, and Character 273.bd

• Label: 273.2.bd
• Level: $273$
• Weight: $2$
• Character orbit: 273.bd
• Rep. character: $\chi_{273}(43,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• Newform subspaces: $2$
• Sturm bound: $74$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bd (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(74\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(273, [\chi])\).

	Total	New	Old
Modular forms	84	32	52
Cusp forms	68	32	36
Eisenstein series	16	0	16

Trace form

32 * q + 20 * q^4 - 16 * q^9 - 8 * q^10 - 12 * q^11 + 16 * q^12 - 8 * q^13 - 12 * q^15 - 20 * q^16 + 8 * q^17 + 24 * q^20 - 20 * q^22 - 8 * q^23 - 8 * q^25 + 40 * q^26 + 12 * q^33 + 4 * q^35 + 20 * q^36 + 12 * q^37 - 56 * q^38 - 8 * q^39 - 88 * q^40 - 12 * q^41 - 4 * q^42 + 4 * q^43 - 12 * q^45 - 12 * q^46 + 16 * q^49 + 60 * q^50 - 24 * q^51 + 4 * q^52 + 40 * q^53 + 12 * q^55 + 12 * q^58 - 84 * q^59 - 4 * q^61 - 4 * q^62 - 32 * q^64 - 64 * q^65 - 32 * q^66 + 12 * q^67 + 16 * q^68 + 4 * q^69 + 24 * q^74 - 16 * q^75 + 48 * q^76 + 16 * q^77 + 24 * q^78 + 88 * q^79 + 144 * q^80 - 16 * q^81 - 60 * q^82 + 24 * q^85 + 24 * q^87 + 60 * q^88 + 96 * q^89 + 16 * q^90 - 8 * q^91 - 136 * q^92 - 8 * q^94 - 28 * q^95 - 60 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(273, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
273.2.bd.a	$273$	$2$	273.bd	13.e	$6$	$16$	$8$	$2.180$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			273.2.bd.a	$2$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(-1+\beta _{12})q^{3}+(1+\beta _{3}+\cdots)q^{4}+\cdots\)
273.2.bd.b	$273$	$2$	273.bd	13.e	$6$	$16$	$8$	$2.180$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			273.2.bd.b	$2$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{14}q^{2}-\beta _{5}q^{3}+(2+2\beta _{5}+\beta _{7}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(273, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(273, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)