Space of modular forms of level 1274, weight 2, and Character 1274.o

• Label: 1274.2.o
• Level: $1274$
• Weight: $2$
• Character orbit: 1274.o
• Rep. character: $\chi_{1274}(459,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $92$
• Newform subspaces: $8$
• Sturm bound: $392$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(392\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1274, [\chi])\).

	Total	New	Old
Modular forms	424	92	332
Cusp forms	360	92	268
Eisenstein series	64	0	64

Trace form

\( 92 q - 2 q^{3} - 92 q^{4} - 36 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1274, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1274.2.o.a	$1274$	$2$	1274.o	91.k	$6$	$4$	$2$	$10.173$	\(\Q(\zeta_{12})\)	None		$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}^{3}q^{2}+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots\)
1274.2.o.b	$1274$	$2$	1274.o	91.k	$6$	$4$	$2$	$10.173$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}^{3}q^{2}+(-\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
1274.2.o.c	$1274$	$2$	1274.o	91.k	$6$	$8$	$4$	$10.173$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{24}^{6}q^{2}+(-\zeta_{24}+\zeta_{24}^{5}+\zeta_{24}^{7})q^{3}+\cdots\)
1274.2.o.d	$1274$	$2$	1274.o	91.k	$6$	$12$	$6$	$10.173$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{5}-\beta _{6})q^{2}-\beta _{10}q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1274.2.o.e	$1274$	$2$	1274.o	91.k	$6$	$12$	$6$	$10.173$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{5}-\beta _{6})q^{2}+\beta _{10}q^{3}-q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
1274.2.o.f	$1274$	$2$	1274.o	91.k	$6$	$16$	$8$	$10.173$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{7}q^{2}+(\beta _{11}+\beta _{12})q^{3}-q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
1274.2.o.g	$1274$	$2$	1274.o	91.k	$6$	$16$	$8$	$10.173$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{11}q^{2}-\beta _{14}q^{3}-q^{4}+(\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
1274.2.o.h	$1274$	$2$	1274.o	91.k	$6$	$20$	$10$	$10.173$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{5}+\beta _{6})q^{2}+\beta _{19}q^{3}-q^{4}+(-\beta _{8}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1274, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1274, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(637, [\chi])\)\(^{\oplus 2}\)