Space of modular forms of level 23, weight 4, and trivial character

• Label: 23.4.a
• Level: $23$
• Weight: $4$
• Character orbit: 23.a
• Rep. character: $\chi_{23}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $2$
• Sturm bound: $8$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	23.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(8\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(23))\).

	Total	New	Old
Modular forms	7	5	2
Cusp forms	5	5	0
Eisenstein series	2	0	2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(23\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(5\)	\(4\)	\(1\)		\(4\)	\(4\)	\(0\)		\(1\)	\(0\)	\(1\)
\(-\)		\(2\)	\(1\)	\(1\)		\(1\)	\(1\)	\(0\)		\(1\)	\(0\)	\(1\)

Trace form

5 * q + 2 * q^3 + 16 * q^4 + 8 * q^5 - 7 * q^6 + 8 * q^7 - 39 * q^8 - 35 * q^9 - 58 * q^10 + 42 * q^11 - 47 * q^12 + 54 * q^13 - 128 * q^14 + 40 * q^15 + 48 * q^16 + 18 * q^17 + 53 * q^18 + 26 * q^19 + 164 * q^20 + 220 * q^21 + 152 * q^22 - 69 * q^23 - 308 * q^24 + 95 * q^25 - 115 * q^26 - 10 * q^27 + 314 * q^28 + 266 * q^29 - 466 * q^30 - 90 * q^31 - 592 * q^32 - 588 * q^33 + 826 * q^34 - 704 * q^35 - 621 * q^36 - 128 * q^37 + 888 * q^38 - 6 * q^39 - 170 * q^40 - 30 * q^41 + 560 * q^42 + 90 * q^43 + 694 * q^44 + 180 * q^45 - 92 * q^46 - 1034 * q^47 + 631 * q^48 + 941 * q^49 + 592 * q^50 + 60 * q^51 + 2475 * q^52 - 644 * q^53 + 351 * q^54 - 1176 * q^55 - 2366 * q^56 + 1672 * q^57 - 2325 * q^58 - 1548 * q^59 - 924 * q^60 + 1576 * q^61 + 237 * q^62 - 1076 * q^63 - 357 * q^64 + 1660 * q^65 - 58 * q^66 + 1414 * q^67 + 604 * q^68 - 276 * q^69 - 3916 * q^70 - 66 * q^71 + 1455 * q^72 + 610 * q^73 + 1962 * q^74 + 1846 * q^75 - 3552 * q^76 + 464 * q^77 - 2477 * q^78 - 2160 * q^79 + 2942 * q^80 - 1603 * q^81 - 1139 * q^82 + 106 * q^83 + 2454 * q^84 + 592 * q^85 + 742 * q^86 + 998 * q^87 + 412 * q^88 + 1882 * q^89 + 1760 * q^90 + 748 * q^91 - 552 * q^92 - 1024 * q^93 + 2281 * q^94 - 536 * q^95 + 1599 * q^96 + 98 * q^97 + 3036 * q^98 - 1566 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(23))\) 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					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		23
23.4.a.a	$23$	$4$	23.a	1.a	$1$	$1$	$1$	$1.357$	\(\Q\)	None	✓	✓	✓	✓	23.4.a.a	$1$	$1$	\(-2\)	\(-5\)	\(-6\)	\(-8\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-5q^{3}-4q^{4}-6q^{5}+10q^{6}+\cdots\)
23.4.a.b	$23$	$4$	23.a	1.a	$1$	$4$	$4$	$1.357$	4.4.334189.1	None	✓	✓	✓	✓	23.4.a.b	$1$	$0$	\(2\)	\(7\)	\(14\)	\(16\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(6+\cdots)q^{4}+\cdots\)