Space of modular forms of level 23, weight 4, and Character 23.c

• Label: 23.4.c
• Level: $23$
• Weight: $4$
• Character orbit: 23.c
• Rep. character: $\chi_{23}(2,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $50$
• Newform subspaces: $1$
• Sturm bound: $8$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	23.c (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(8\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(23, [\chi])\).

	Total	New	Old
Modular forms	70	70	0
Cusp forms	50	50	0
Eisenstein series	20	20	0

Trace form

50 * q - 11 * q^2 - 13 * q^3 - 27 * q^4 - 19 * q^5 - 4 * q^6 - 19 * q^7 + 28 * q^8 + 24 * q^9 + 47 * q^10 - 53 * q^11 + 36 * q^12 - 65 * q^13 + 117 * q^14 - 425 * q^15 - 499 * q^16 - 117 * q^17 + 24 * q^18 + 73 * q^19 + 529 * q^20 + 429 * q^21 + 310 * q^22 + 542 * q^23 + 1606 * q^24 + 246 * q^25 + 324 * q^26 + 65 * q^27 - 677 * q^28 - 497 * q^29 - 1041 * q^30 - 471 * q^31 - 915 * q^32 - 391 * q^33 - 2751 * q^34 - 737 * q^35 - 1865 * q^36 - 1071 * q^37 - 1504 * q^38 + 127 * q^39 + 1479 * q^40 + 569 * q^41 + 3059 * q^42 + 1615 * q^43 + 2518 * q^44 + 2768 * q^45 + 4041 * q^46 + 2904 * q^47 + 2702 * q^48 + 1226 * q^49 + 1322 * q^50 + 589 * q^51 - 2156 * q^52 + 391 * q^53 - 5862 * q^54 - 3323 * q^55 - 7028 * q^56 - 7623 * q^57 - 5639 * q^58 - 2445 * q^59 - 3157 * q^60 - 1059 * q^61 + 1468 * q^62 + 3155 * q^63 + 4570 * q^64 + 2641 * q^65 + 5206 * q^66 + 27 * q^67 + 8350 * q^68 + 4005 * q^69 + 9702 * q^70 + 3465 * q^71 + 5629 * q^72 + 435 * q^73 - 994 * q^74 - 7819 * q^75 - 3598 * q^76 - 5931 * q^77 - 8996 * q^78 - 2559 * q^79 - 14052 * q^80 - 4788 * q^81 - 3822 * q^82 - 3967 * q^83 - 8427 * q^84 + 299 * q^85 + 721 * q^86 + 8363 * q^87 + 5825 * q^88 + 3717 * q^89 + 16742 * q^90 + 7238 * q^91 + 9550 * q^92 + 12750 * q^93 + 6035 * q^94 + 4551 * q^95 + 2493 * q^96 - 2419 * q^97 - 5687 * q^98 - 755 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(23, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
23.4.c.a	$23$	$4$	23.c	23.c	$11$	$50$	$5$	$1.357$		None		✓	✓	✓	23.4.c.a	$2$	$0$	\(-11\)	\(-13\)	\(-19\)	\(-19\)		$\mathrm{SU}(2)[C_{11}]$