Space of modular forms of level 2254, weight 2, and Character 2254.c

• Label: 2254.2.c
• Level: $2254$
• Weight: $2$
• Character orbit: 2254.c
• Rep. character: $\chi_{2254}(2253,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $5$
• Sturm bound: $672$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 2254 = 2 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2254.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 161 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(672\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2254, [\chi])\).

	Total	New	Old
Modular forms	352	80	272
Cusp forms	320	80	240
Eisenstein series	32	0	32

Trace form

80 * q + 80 * q^4 - 88 * q^9 + 80 * q^16 + 32 * q^18 - 8 * q^23 + 104 * q^25 + 32 * q^29 - 88 * q^36 - 8 * q^39 - 8 * q^46 + 32 * q^50 + 80 * q^64 + 32 * q^72 + 16 * q^78 + 64 * q^81 + 104 * q^85 - 8 * q^92 + 96 * q^93 + 56 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(2254, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2254.2.c.a	$2254$	$2$	2254.c	161.c	$2$	$8$	$8$	$17.998$	8.0.\(\cdots\).12	None		✓			2254.2.c.a	$4$	$0$	\(8\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+(\beta _{3}-\beta _{7})q^{3}+q^{4}+\beta _{4}q^{5}+\cdots\)
2254.2.c.b	$2254$	$2$	2254.c	161.c	$2$	$16$	$16$	$17.998$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					322.2.g.b	$4$	$0$	\(-16\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-\beta _{13}q^{3}+q^{4}+(-\beta _{2}+\beta _{10}+\cdots)q^{5}+\cdots\)
2254.2.c.c	$2254$	$2$	2254.c	161.c	$2$	$16$	$16$	$17.998$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					322.2.g.a	$4$	$0$	\(16\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+\beta _{3}q^{3}+q^{4}+\beta _{11}q^{5}+\beta _{3}q^{6}+\cdots\)
2254.2.c.d	$2254$	$2$	2254.c	161.c	$2$	$16$	$16$	$17.998$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			2254.2.c.d	$4$	$0$	\(16\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+\beta _{6}q^{3}+q^{4}-\beta _{7}q^{5}+\beta _{6}q^{6}+\cdots\)
2254.2.c.e	$2254$	$2$	2254.c	161.c	$2$	$24$	$24$	$17.998$		None		✓	✓		2254.2.c.e	$4$	$0$	\(-24\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2254, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2254, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(322, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1127, [\chi])\)\(^{\oplus 2}\)