Space of modular forms of level 454, weight 2, and Character 454.c

• Label: 454.2.c
• Level: $454$
• Weight: $2$
• Character orbit: 454.c
• Rep. character: $\chi_{454}(3,\cdot)$
• Character field: $\Q(\zeta_{113})$
• Dimension: $2128$
• Newform subspaces: $2$
• Sturm bound: $114$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$454 = 2 \cdot 227$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	454.c (of order $113$ and degree $112$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$227$
Character field:			$\Q(\zeta_{113})$
Newform subspaces:			$2$
Sturm bound:			$114$
Trace bound:			$1$
Distinguishing $T_p$:			$3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(454, [\chi])$.

	Total	New	Old
Modular forms	6608	2128	4480
Cusp forms	6160	2128	4032
Eisenstein series	448	0	448

Trace form

2128 * q - q^2 - 2 * q^3 - 19 * q^4 - 2 * q^5 - 8 * q^6 - 4 * q^7 - q^8 - 33 * q^9 - 4 * q^10 - 10 * q^11 - 2 * q^12 - 10 * q^13 - 12 * q^14 - 28 * q^15 - 19 * q^16 - 14 * q^17 - 21 * q^18 - 18 * q^19 - 2 * q^20 - 36 * q^21 - 16 * q^22 - 36 * q^23 - 8 * q^24 - 39 * q^25 - 12 * q^26 - 32 * q^27 - 4 * q^28 - 48 * q^29 - 12 * q^30 - 24 * q^31 - q^32 - 56 * q^33 - 6 * q^34 - 20 * q^35 - 33 * q^36 - 14 * q^37 - 20 * q^38 - 48 * q^39 - 4 * q^40 - 42 * q^41 - 44 * q^42 - 42 * q^43 - 10 * q^44 - 46 * q^45 - 28 * q^46 - 72 * q^47 - 2 * q^48 - 55 * q^49 - 39 * q^50 - 84 * q^51 - 10 * q^52 - 48 * q^53 - 56 * q^54 - 56 * q^55 - 12 * q^56 - 70 * q^57 - 30 * q^58 - 68 * q^59 - 28 * q^60 - 42 * q^61 - 32 * q^62 - 86 * q^63 - 19 * q^64 - 120 * q^65 - 48 * q^66 - 68 * q^67 - 14 * q^68 - 74 * q^69 - 60 * q^70 - 72 * q^71 - 21 * q^72 - 50 * q^73 - 16 * q^74 - 110 * q^75 - 18 * q^76 - 146 * q^77 - 16 * q^78 - 68 * q^79 - 2 * q^80 - 139 * q^81 - 30 * q^82 - 112 * q^83 - 36 * q^84 - 56 * q^85 - 48 * q^86 - 142 * q^87 - 16 * q^88 - 58 * q^89 - 52 * q^90 - 80 * q^91 - 36 * q^92 - 68 * q^93 - 36 * q^94 - 156 * q^95 - 8 * q^96 - 62 * q^97 - 33 * q^98 - 144 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(454, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
454.2.c.a	$454$	$2$	454.c	227.c	$113$	$1008$	$9$	$3.625$		None		✓			454.2.c.a	$2$	$0$	$9$	$3$	$1$	$4$		$\mathrm{SU}(2)[C_{113}]$
454.2.c.b	$454$	$2$	454.c	227.c	$113$	$1120$	$10$	$3.625$		None		✓	✓		454.2.c.b	$2$	$0$	$-10$	$-5$	$-3$	$-8$		$\mathrm{SU}(2)[C_{113}]$

Decomposition of $S_{2}^{\mathrm{old}}(454, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(454, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(227, [\chi])$$^{\oplus 2}$