Space of modular forms of level 183, weight 2, and trivial character

• Label: 183.2.a
• Level: $183$
• Weight: $2$
• Character orbit: 183.a
• Rep. character: $\chi_{183}(1,\cdot)$
• Character field: $\Q$
• Dimension: $11$
• Newform subspaces: $3$
• Sturm bound: $41$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$183 = 3 \cdot 61$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	183.a (trivial)
Character field:			$\Q$
Newform subspaces:			$3$
Sturm bound:			$41$
Trace bound:			$1$
Distinguishing $T_p$:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(183))$.

	Total	New	Old
Modular forms	22	11	11
Cusp forms	19	11	8
Eisenstein series	3	0	3

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

$3$	$61$	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
$+$	$+$	$+$		$3$	$2$	$1$		$3$	$2$	$1$		$0$	$0$	$0$
$+$	$-$	$-$		$7$	$3$	$4$		$6$	$3$	$3$		$1$	$0$	$1$
$-$	$+$	$-$		$8$	$6$	$2$		$7$	$6$	$1$		$1$	$0$	$1$
$-$	$-$	$+$		$4$	$0$	$4$		$3$	$0$	$3$		$1$	$0$	$1$
Plus space		$+$		$7$	$2$	$5$		$6$	$2$	$4$		$1$	$0$	$1$
Minus space		$-$		$15$	$9$	$6$		$13$	$9$	$4$		$2$	$0$	$2$

Trace form

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

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(183))$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	61
183.2.a.a	$183$	$2$	183.a	1.a	$1$	$2$	$2$	$1.461$	$\Q(\sqrt{2})$	None	✓	✓	✓	✓	183.2.a.a	$1$	$1$	$-2$	$-2$	$-2$	$-2$		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots$
183.2.a.b	$183$	$2$	183.a	1.a	$1$	$3$	$3$	$1.461$	3.3.148.1	None	✓	✓	✓	✓	183.2.a.b	$1$	$0$	$1$	$-3$	$6$	$0$		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+2q^{5}+\cdots$
183.2.a.c	$183$	$2$	183.a	1.a	$1$	$6$	$6$	$1.461$	6.6.91407488.1	None	✓	✓	✓	✓	183.2.a.c	$1$	$0$	$0$	$6$	$2$	$2$		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(183))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_0(183)) \simeq$ $S_{2}^{\mathrm{new}}(\Gamma_0(61))$$^{\oplus 2}$