Space of modular forms of level 4011, weight 2, and trivial character

• Label: 4011.2.a
• Level: $4011$
• Weight: $2$
• Character orbit: 4011.a
• Rep. character: $\chi_{4011}(1,\cdot)$
• Character field: $\Q$
• Dimension: $191$
• Newform subspaces: $13$
• Sturm bound: $1024$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(1024\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4011))\).

	Total	New	Old
Modular forms	516	191	325
Cusp forms	509	191	318
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.

\(3\)	\(7\)	\(191\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(19\)
\(+\)	\(+\)	\(-\)	$-$	\(29\)
\(+\)	\(-\)	\(+\)	$-$	\(29\)
\(+\)	\(-\)	\(-\)	$+$	\(19\)
\(-\)	\(+\)	\(+\)	$-$	\(29\)
\(-\)	\(+\)	\(-\)	$+$	\(19\)
\(-\)	\(-\)	\(+\)	$+$	\(19\)
\(-\)	\(-\)	\(-\)	$-$	\(28\)
Plus space			\(+\)	\(76\)
Minus space			\(-\)	\(115\)

Trace form

\( 191 q + q^{2} - q^{3} + 197 q^{4} + 10 q^{5} + 5 q^{6} - q^{7} - 3 q^{8} + 191 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4011))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	7	191
4011.2.a.a	$4011$	$2$	4011.a	1.a	$1$	$1$	$1$	$32.028$	\(\Q\)	None	✓	$1$	$0$	\(-2\)	\(1\)	\(1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+q^{7}+\cdots\)
4011.2.a.b	$4011$	$2$	4011.a	1.a	$1$	$1$	$1$	$32.028$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(1\)	\(-1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
4011.2.a.c	$4011$	$2$	4011.a	1.a	$1$	$1$	$1$	$32.028$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}-4q^{5}-q^{7}+q^{9}-3q^{11}+\cdots\)
4011.2.a.d	$4011$	$2$	4011.a	1.a	$1$	$1$	$1$	$32.028$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(-1\)	\(4\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}+4q^{5}-2q^{6}+\cdots\)
4011.2.a.e	$4011$	$2$	4011.a	1.a	$1$	$3$	$3$	$32.028$	3.3.229.1	None	✓	$1$	$0$	\(0\)	\(-3\)	\(2\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
4011.2.a.f	$4011$	$2$	4011.a	1.a	$1$	$18$	$18$	$32.028$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	$1$	$1$	\(-6\)	\(18\)	\(-21\)	\(18\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
4011.2.a.g	$4011$	$2$	4011.a	1.a	$1$	$18$	$18$	$32.028$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	$1$	$1$	\(-3\)	\(18\)	\(-10\)	\(-18\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{10}+\cdots)q^{5}+\cdots\)
4011.2.a.h	$4011$	$2$	4011.a	1.a	$1$	$19$	$19$	$32.028$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	$1$	$1$	\(-1\)	\(-19\)	\(-4\)	\(-19\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
4011.2.a.i	$4011$	$2$	4011.a	1.a	$1$	$19$	$19$	$32.028$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	$1$	$1$	\(3\)	\(-19\)	\(-12\)	\(19\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{8}+\cdots)q^{5}+\cdots\)
4011.2.a.j	$4011$	$2$	4011.a	1.a	$1$	$26$	$26$	$32.028$		None	✓	$1$	$0$	\(0\)	\(-26\)	\(2\)	\(-26\)		$+$	$+$	$-$	$-$		$\mathrm{SU}(2)$
4011.2.a.k	$4011$	$2$	4011.a	1.a	$1$	$27$	$27$	$32.028$		None	✓	$1$	$0$	\(9\)	\(27\)	\(23\)	\(27\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$
4011.2.a.l	$4011$	$2$	4011.a	1.a	$1$	$28$	$28$	$32.028$		None	✓	$1$	$0$	\(-6\)	\(-28\)	\(8\)	\(28\)		$+$	$-$	$+$	$-$		$\mathrm{SU}(2)$
4011.2.a.m	$4011$	$2$	4011.a	1.a	$1$	$29$	$29$	$32.028$		None	✓	$1$	$0$	\(6\)	\(29\)	\(22\)	\(-29\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4011))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4011)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(191))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(573))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1337))\)\(^{\oplus 2}\)