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 + 4 * q^10 - 4 * q^13 - 48 * q^16 + 10 * q^17 + 4 * q^22 - 24 * q^23 + 48 * q^25 + 6 * q^26 + 12 * q^27 - 44 * q^29 + 22 * q^30 - 136 * q^36 + 14 * q^38 - 4 * q^40 + 136 * q^43 + 30 * q^51 - 2 * q^52 + 42 * q^53 + 40 * q^55 + 26 * q^61 - 12 * q^62 - 96 * q^64 - 4 * q^65 + 16 * q^66 - 10 * q^68 - 8 * q^69 - 16 * q^74 - 56 * q^75 - 32 * q^78 + 100 * q^79 - 88 * q^81 - 8 * q^82 - 32 * q^87 + 2 * q^88 - 52 * q^90 - 48 * q^92 - 22 * q^94 - 16 * q^95

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1274.2.n.a	$1274$	$2$	1274.n	91.r	$6$	$4$	$2$	$10.173$	\(\Q(\zeta_{12})\)	None		✓			1274.2.d.a	$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}-3\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
1274.2.n.b	$1274$	$2$	1274.n	91.r	$6$	$4$	$2$	$10.173$	\(\Q(\zeta_{12})\)	None					182.2.d.a	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}-\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}-2\zeta_{12}q^{5}+\cdots\)
1274.2.n.c	$1274$	$2$	1274.n	91.r	$6$	$4$	$2$	$10.173$	\(\Q(\zeta_{12})\)	None					26.2.b.a	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}-\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+3\zeta_{12}q^{5}+\cdots\)
1274.2.n.d	$1274$	$2$	1274.n	91.r	$6$	$4$	$2$	$10.173$	\(\Q(\zeta_{12})\)	None					26.2.b.a	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+3\zeta_{12}q^{5}+\cdots\)
1274.2.n.e	$1274$	$2$	1274.n	91.r	$6$	$4$	$2$	$10.173$	\(\Q(\zeta_{12})\)	None					182.2.d.a	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}-2\zeta_{12}q^{5}+\cdots\)
1274.2.n.f	$1274$	$2$	1274.n	91.r	$6$	$4$	$2$	$10.173$	\(\Q(\zeta_{12})\)	None					182.2.n.a	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+2\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
1274.2.n.g	$1274$	$2$	1274.n	91.r	$6$	$4$	$2$	$10.173$	\(\Q(\zeta_{12})\)	None		✓			1274.2.d.a	$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(3-3\zeta_{12}^{2})q^{3}+\cdots\)
1274.2.n.h	$1274$	$2$	1274.n	91.r	$6$	$8$	$4$	$10.173$	\(\Q(\zeta_{24})\)	None		✓			1274.2.d.g	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta_{3}-\beta_1)q^{2}+(\beta_{7}-\beta_{4}+\beta_{2}-1)q^{3}+\cdots\)
1274.2.n.i	$1274$	$2$	1274.n	91.r	$6$	$8$	$4$	$10.173$	\(\Q(\zeta_{24})\)	None		✓			1274.2.d.i	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{24}^{2}q^{2}+(2\zeta_{24}+2\zeta_{24}^{7})q^{3}+\zeta_{24}^{4}q^{4}+\cdots\)
1274.2.n.j	$1274$	$2$	1274.n	91.r	$6$	$8$	$4$	$10.173$	\(\Q(\zeta_{24})\)	None		✓			1274.2.d.h	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{24}^{2}+\zeta_{24}^{6})q^{2}+(\zeta_{24}^{3}-\zeta_{24}^{5}+\cdots)q^{3}+\cdots\)
1274.2.n.k	$1274$	$2$	1274.n	91.r	$6$	$8$	$4$	$10.173$	\(\Q(\zeta_{24})\)	None		✓			1274.2.d.g	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta_1 q^{2}+(\beta_{4}+\beta_{2})q^{3}+\beta_{2} q^{4}+\cdots\)
1274.2.n.l	$1274$	$2$	1274.n	91.r	$6$	$12$	$6$	$10.173$	12.0.\(\cdots\).1	None					182.2.n.b	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{10}q^{2}+(-1-\beta _{4}+\beta _{7})q^{3}+(1+\cdots)q^{4}+\cdots\)
1274.2.n.m	$1274$	$2$	1274.n	91.r	$6$	$12$	$6$	$10.173$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					182.2.d.b	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{3}+\beta _{8})q^{2}+(-\beta _{2}-\beta _{11})q^{3}+\cdots\)
1274.2.n.n	$1274$	$2$	1274.n	91.r	$6$	$12$	$6$	$10.173$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					182.2.d.b	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{2}-\beta _{11}q^{3}-\beta _{9}q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots\)

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

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