Space of modular forms of level 1911, weight 2, and trivial character

• Label: 1911.2.a
• Level: $1911$
• Weight: $2$
• Character orbit: 1911.a
• Rep. character: $\chi_{1911}(1,\cdot)$
• Character field: $\Q$
• Dimension: $82$
• Newform subspaces: $25$
• Sturm bound: $522$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1911.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 25 \)
Sturm bound:			\(522\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1911))\).

	Total	New	Old
Modular forms	276	82	194
Cusp forms	245	82	163
Eisenstein series	31	0	31

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

\(3\)	\(7\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(7\)
\(+\)	\(+\)	\(-\)	\(-\)	\(13\)
\(+\)	\(-\)	\(+\)	\(-\)	\(12\)
\(+\)	\(-\)	\(-\)	\(+\)	\(9\)
\(-\)	\(+\)	\(+\)	\(-\)	\(15\)
\(-\)	\(+\)	\(-\)	\(+\)	\(5\)
\(-\)	\(-\)	\(+\)	\(+\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)	\(15\)
Plus space			\(+\)	\(27\)
Minus space			\(-\)	\(55\)

Trace form

\( 82 q + 4 q^{2} + 82 q^{4} + 4 q^{5} - 2 q^{6} + 24 q^{8} + 82 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1911))\) 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	7	13
1911.2.a.a	$1911$	$2$	1911.a	1.a	$1$	$1$	$1$	$15.259$	\(\Q\)	None	✓				273.2.a.a	$1$	$1$	\(-2\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+q^{9}+\cdots\)
1911.2.a.b	$1911$	$2$	1911.a	1.a	$1$	$1$	$1$	$15.259$	\(\Q\)	None	✓				273.2.i.a	$1$	$1$	\(-1\)	\(-1\)	\(-4\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}-4q^{5}+q^{6}+3q^{8}+\cdots\)
1911.2.a.c	$1911$	$2$	1911.a	1.a	$1$	$1$	$1$	$15.259$	\(\Q\)	None	✓				273.2.i.a	$1$	$0$	\(-1\)	\(1\)	\(4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}+4q^{5}-q^{6}+3q^{8}+\cdots\)
1911.2.a.d	$1911$	$2$	1911.a	1.a	$1$	$1$	$1$	$15.259$	\(\Q\)	None	✓	✓			1911.2.a.d	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}-q^{5}+q^{9}-2q^{11}+2q^{12}+\cdots\)
1911.2.a.e	$1911$	$2$	1911.a	1.a	$1$	$1$	$1$	$15.259$	\(\Q\)	None	✓	✓			1911.2.a.d	$1$	$1$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+q^{5}+q^{9}-2q^{11}-2q^{12}+\cdots\)
1911.2.a.f	$1911$	$2$	1911.a	1.a	$1$	$1$	$1$	$15.259$	\(\Q\)	None	✓				39.2.a.a	$1$	$1$	\(1\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}-3q^{8}+\cdots\)
1911.2.a.g	$1911$	$2$	1911.a	1.a	$1$	$1$	$1$	$15.259$	\(\Q\)	None	✓				273.2.a.b	$1$	$1$	\(2\)	\(-1\)	\(-1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}+q^{9}+\cdots\)
1911.2.a.h	$1911$	$2$	1911.a	1.a	$1$	$2$	$2$	$15.259$	\(\Q(\sqrt{2}) \)	None	✓				39.2.a.b	$1$	$1$	\(-2\)	\(-2\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+2\beta q^{5}+\cdots\)
1911.2.a.i	$1911$	$2$	1911.a	1.a	$1$	$2$	$2$	$15.259$	\(\Q(\sqrt{2}) \)	None	✓	✓			1911.2.a.i	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+q^{5}-\beta q^{6}-2\beta q^{8}+\cdots\)
1911.2.a.j	$1911$	$2$	1911.a	1.a	$1$	$2$	$2$	$15.259$	\(\Q(\sqrt{2}) \)	None	✓	✓			1911.2.a.i	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}-q^{5}+\beta q^{6}-2\beta q^{8}+\cdots\)
1911.2.a.k	$1911$	$2$	1911.a	1.a	$1$	$2$	$2$	$15.259$	\(\Q(\sqrt{2}) \)	None	✓				273.2.a.c	$1$	$0$	\(2\)	\(2\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+(1+\beta )q^{6}+\cdots\)
1911.2.a.l	$1911$	$2$	1911.a	1.a	$1$	$3$	$3$	$15.259$	\(\Q(\zeta_{14})^+\)	None	✓				273.2.i.c	$1$	$0$	\(-2\)	\(-3\)	\(3\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
1911.2.a.m	$1911$	$2$	1911.a	1.a	$1$	$3$	$3$	$15.259$	\(\Q(\zeta_{14})^+\)	None	✓		✓		273.2.i.c	$1$	$1$	\(-2\)	\(3\)	\(-3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
1911.2.a.n	$1911$	$2$	1911.a	1.a	$1$	$3$	$3$	$15.259$	3.3.316.1	None	✓				273.2.a.d	$1$	$0$	\(-2\)	\(3\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+q^{3}+(2-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
1911.2.a.o	$1911$	$2$	1911.a	1.a	$1$	$3$	$3$	$15.259$	\(\Q(\zeta_{18})^+\)	None	✓				273.2.i.b	$1$	$0$	\(0\)	\(-3\)	\(3\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(1+\beta _{1})q^{5}+\cdots\)
1911.2.a.p	$1911$	$2$	1911.a	1.a	$1$	$3$	$3$	$15.259$	\(\Q(\zeta_{18})^+\)	None	✓		✓		273.2.i.b	$1$	$1$	\(0\)	\(3\)	\(-3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
1911.2.a.q	$1911$	$2$	1911.a	1.a	$1$	$4$	$4$	$15.259$	4.4.69777.1	None	✓		✓		273.2.i.d	$1$	$1$	\(-1\)	\(-4\)	\(-3\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
1911.2.a.r	$1911$	$2$	1911.a	1.a	$1$	$4$	$4$	$15.259$	4.4.69777.1	None	✓				273.2.i.d	$1$	$0$	\(-1\)	\(4\)	\(3\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
1911.2.a.s	$1911$	$2$	1911.a	1.a	$1$	$4$	$4$	$15.259$	4.4.17428.1	None	✓				273.2.a.e	$1$	$0$	\(1\)	\(-4\)	\(3\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
1911.2.a.t	$1911$	$2$	1911.a	1.a	$1$	$5$	$5$	$15.259$	5.5.375116.1	None	✓		✓		273.2.i.e	$1$	$1$	\(0\)	\(-5\)	\(-3\)	\(0\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}-q^{3}+(1-\beta _{4})q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)
1911.2.a.u	$1911$	$2$	1911.a	1.a	$1$	$5$	$5$	$15.259$	5.5.375116.1	None	✓				273.2.i.e	$1$	$0$	\(0\)	\(5\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+q^{3}+(1-\beta _{4})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
1911.2.a.v	$1911$	$2$	1911.a	1.a	$1$	$5$	$5$	$15.259$	5.5.2196544.1	None	✓	✓	✓		1911.2.a.v	$1$	$0$	\(2\)	\(-5\)	\(-3\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{4})q^{5}+\cdots\)
1911.2.a.w	$1911$	$2$	1911.a	1.a	$1$	$5$	$5$	$15.259$	5.5.2196544.1	None	✓	✓			1911.2.a.v	$1$	$0$	\(2\)	\(5\)	\(3\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{4})q^{5}+\cdots\)
1911.2.a.x	$1911$	$2$	1911.a	1.a	$1$	$10$	$10$	$15.259$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓	✓		1911.2.a.x	$1$	$0$	\(4\)	\(-10\)	\(6\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{5}+\cdots)q^{5}+\cdots\)
1911.2.a.y	$1911$	$2$	1911.a	1.a	$1$	$10$	$10$	$15.259$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓	✓		1911.2.a.x	$1$	$0$	\(4\)	\(10\)	\(-6\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(-1-\beta _{5}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1911))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1911)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(637))\)\(^{\oplus 2}\)