Space of modular forms of level 136, weight 2, and trivial character

• Label: 136.2.a
• Level: $136$
• Weight: $2$
• Character orbit: 136.a
• Rep. character: $\chi_{136}(1,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $3$
• Sturm bound: $36$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	136.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(36\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(136))\).

	Total	New	Old
Modular forms	22	4	18
Cusp forms	15	4	11
Eisenstein series	7	0	7

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

\(2\)	\(17\)	Fricke	Dim
\(+\)	\(-\)	\(-\)	\(2\)
\(-\)	\(+\)	\(-\)	\(1\)
\(-\)	\(-\)	\(+\)	\(1\)
Plus space		\(+\)	\(1\)
Minus space		\(-\)	\(3\)

Trace form

4 * q - 2 * q^3 + 2 * q^5 + 8 * q^9 - 2 * q^11 - 4 * q^13 + 2 * q^17 - 8 * q^21 + 12 * q^23 - 8 * q^25 - 20 * q^27 - 6 * q^29 - 8 * q^31 + 4 * q^33 + 8 * q^35 - 2 * q^37 + 4 * q^39 + 4 * q^41 - 12 * q^43 + 10 * q^45 - 12 * q^49 - 6 * q^51 - 4 * q^53 + 16 * q^55 - 8 * q^57 + 12 * q^59 + 22 * q^61 + 24 * q^63 - 4 * q^65 - 12 * q^67 - 16 * q^69 + 28 * q^71 - 6 * q^75 + 24 * q^77 - 4 * q^79 + 36 * q^83 + 2 * q^85 + 16 * q^87 - 24 * q^89 - 24 * q^91 - 8 * q^93 - 8 * q^95 - 12 * q^97 + 22 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(136))\) 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	17
136.2.a.a	$136$	$2$	136.a	1.a	$1$	$1$	$1$	$1.086$	\(\Q\)	None	✓	✓	✓	✓	136.2.a.a	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{5}-2q^{7}+q^{9}-6q^{11}+\cdots\)
136.2.a.b	$136$	$2$	136.a	1.a	$1$	$1$	$1$	$1.086$	\(\Q\)	None	✓	✓	✓	✓	136.2.a.b	$1$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{9}+2q^{11}-6q^{13}-q^{17}+\cdots\)
136.2.a.c	$136$	$2$	136.a	1.a	$1$	$2$	$2$	$1.086$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓	✓	136.2.a.c	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(2\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+2q^{5}+(1+\beta )q^{7}+(3+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(136))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(136)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 2}\)