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

• Label: 1274.2.n
• Level: $1274$
• Weight: $2$
• Character orbit: 1274.n
• Rep. character: $\chi_{1274}(753,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $14$
• Sturm bound: $392$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(392\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

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

	Total	New	Old
Modular forms	424	96	328
Cusp forms	360	96	264
Eisenstein series	64	0	64

Trace form

\( 96 q + 48 q^{4} - 68 q^{9} + O(q^{10}) \)

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.n.a	$1274$	$2$	1274.n	91.r	$6$	$4$	$2$	$10.173$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}-3\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
1274.2.n.b	$1274$	$2$	1274.n	91.r	$6$	$4$	$2$	$10.173$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}-\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}-2\zeta_{12}q^{5}+\cdots\)
1274.2.n.c	$1274$	$2$	1274.n	91.r	$6$	$4$	$2$	$10.173$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}-\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+3\zeta_{12}q^{5}+\cdots\)
1274.2.n.d	$1274$	$2$	1274.n	91.r	$6$	$4$	$2$	$10.173$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+3\zeta_{12}q^{5}+\cdots\)
1274.2.n.e	$1274$	$2$	1274.n	91.r	$6$	$4$	$2$	$10.173$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}-2\zeta_{12}q^{5}+\cdots\)
1274.2.n.f	$1274$	$2$	1274.n	91.r	$6$	$4$	$2$	$10.173$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+2\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
1274.2.n.g	$1274$	$2$	1274.n	91.r	$6$	$4$	$2$	$10.173$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(3-3\zeta_{12}^{2})q^{3}+\cdots\)
1274.2.n.h	$1274$	$2$	1274.n	91.r	$6$	$8$	$4$	$10.173$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{24}+\zeta_{24}^{3})q^{2}+(-1+\zeta_{24}^{2}+\cdots)q^{3}+\cdots\)
1274.2.n.i	$1274$	$2$	1274.n	91.r	$6$	$8$	$4$	$10.173$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{24}^{2}q^{2}+(2\zeta_{24}+2\zeta_{24}^{7})q^{3}+\zeta_{24}^{4}q^{4}+\cdots\)
1274.2.n.j	$1274$	$2$	1274.n	91.r	$6$	$8$	$4$	$10.173$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{24}^{2}+\zeta_{24}^{6})q^{2}+(\zeta_{24}^{3}-\zeta_{24}^{5}+\cdots)q^{3}+\cdots\)
1274.2.n.k	$1274$	$2$	1274.n	91.r	$6$	$8$	$4$	$10.173$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{24}q^{2}+(\zeta_{24}^{2}+\zeta_{24}^{4})q^{3}+\zeta_{24}^{2}q^{4}+\cdots\)
1274.2.n.l	$1274$	$2$	1274.n	91.r	$6$	$12$	$6$	$10.173$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{10}q^{2}+(-1-\beta _{4}+\beta _{7})q^{3}+(1+\cdots)q^{4}+\cdots\)
1274.2.n.m	$1274$	$2$	1274.n	91.r	$6$	$12$	$6$	$10.173$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{3}+\beta _{8})q^{2}+(-\beta _{2}-\beta _{11})q^{3}+\cdots\)
1274.2.n.n	$1274$	$2$	1274.n	91.r	$6$	$12$	$6$	$10.173$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{2}-\beta _{11}q^{3}-\beta _{9}q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots\)

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

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