Space of modular forms of level 261, weight 2, and Character 261.o

• Label: 261.2.o
• Level: $261$
• Weight: $2$
• Character orbit: 261.o
• Rep. character: $\chi_{261}(64,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $72$
• Newform subspaces: $3$
• Sturm bound: $60$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.o (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(60\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(261, [\chi])\).

	Total	New	Old
Modular forms	204	84	120
Cusp forms	156	72	84
Eisenstein series	48	12	36

Trace form

\( 72 q + 7 q^{2} + 9 q^{4} + 5 q^{5} - 3 q^{7} - 14 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(261, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
261.2.o.a	$261$	$2$	261.o	29.e	$14$	$12$	$2$	$2.084$	12.0.\(\cdots\).1	None		$2$	$0$	\(7\)	\(0\)	\(1\)	\(-11\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q+(1-\beta _{3}-\beta _{7}-\beta _{9}-\beta _{10})q^{2}+(\beta _{1}+\cdots)q^{4}+\cdots\)
261.2.o.b	$261$	$2$	261.o	29.e	$14$	$24$	$4$	$2.084$		None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(8\)		$\mathrm{SU}(2)[C_{14}]$
261.2.o.c	$261$	$2$	261.o	29.e	$14$	$36$	$6$	$2.084$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{14}]$

Decomposition of \(S_{2}^{\mathrm{old}}(261, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(261, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 2}\)