Space of modular forms of level 20, weight 12, and trivial character

• Label: 20.12.a
• Level: $20$
• Weight: $12$
• Character orbit: 20.a
• Rep. character: $\chi_{20}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $36$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	20.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(36\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(20))\).

	Total	New	Old
Modular forms	36	3	33
Cusp forms	30	3	27
Eisenstein series	6	0	6

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

\(2\)	\(5\)	Fricke	Dim
\(-\)	\(+\)	\(-\)	\(1\)
\(-\)	\(-\)	\(+\)	\(2\)
Plus space		\(+\)	\(2\)
Minus space		\(-\)	\(1\)

Trace form

3 * q + 526 * q^3 + 3125 * q^5 - 28734 * q^7 - 39773 * q^9 + 293040 * q^11 + 1437654 * q^13 - 268750 * q^15 + 3959022 * q^17 + 3160332 * q^19 + 32048108 * q^21 + 22871382 * q^23 + 29296875 * q^25 - 31679468 * q^27 + 39728922 * q^29 + 153568188 * q^31 - 114594960 * q^33 + 110668750 * q^35 - 838367994 * q^37 - 977016388 * q^39 + 593660058 * q^41 - 16928250 * q^43 + 397653125 * q^45 - 1145164758 * q^47 - 291676881 * q^49 - 2443209204 * q^51 + 3824525838 * q^53 + 948750000 * q^55 + 2831715224 * q^57 + 6558500604 * q^59 - 4737293274 * q^61 + 11880551714 * q^63 + 3068706250 * q^65 + 2526990306 * q^67 - 1519195644 * q^69 - 55526135916 * q^71 + 51700617654 * q^73 + 5136718750 * q^75 - 15515642160 * q^77 - 32040411384 * q^79 - 61073448953 * q^81 + 56064195942 * q^83 + 44230181250 * q^85 - 121965495516 * q^87 - 9837283362 * q^89 - 136246479228 * q^91 + 256570464296 * q^93 + 111620012500 * q^95 - 89661136554 * q^97 - 25109887440 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(20))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	5
20.12.a.a	$20$	$12$	20.a	1.a	$1$	$1$	$1$	$15.367$	\(\Q\)	None	✓	✓	✓	✓	20.12.a.a	$1$	$1$	\(0\)	\(306\)	\(-3125\)	\(-32074\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+306q^{3}-5^{5}q^{5}-32074q^{7}-83511q^{9}+\cdots\)
20.12.a.b	$20$	$12$	20.a	1.a	$1$	$2$	$2$	$15.367$	\(\Q(\sqrt{46729}) \)	None	✓	✓	✓	✓	20.12.a.b	$1$	$0$	\(0\)	\(220\)	\(6250\)	\(3340\)		$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(110-\beta )q^{3}+5^{5}q^{5}+(1670-111\beta )q^{7}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(20))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(20)) \simeq \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 2}\)