Space of modular forms of level 1331, weight 2, and trivial character

• Label: 1331.2.a
• Level: $1331$
• Weight: $2$
• Character orbit: 1331.a
• Rep. character: $\chi_{1331}(1,\cdot)$
• Character field: $\Q$
• Dimension: $100$
• Newform subspaces: $6$
• Sturm bound: $242$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1331 = 11^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1331.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(242\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1331))\).

	Total	New	Old
Modular forms	132	100	32
Cusp forms	111	100	11
Eisenstein series	21	0	21

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

\(11\)	Dim
\(+\)	\(40\)
\(-\)	\(60\)

Trace form

100 * q - q^3 + 100 * q^4 - q^5 + 99 * q^9 - 4 * q^12 - 4 * q^14 - 5 * q^15 + 96 * q^16 - 8 * q^20 - 3 * q^23 + 97 * q^25 - 6 * q^26 - 7 * q^27 - 5 * q^31 - 8 * q^34 + 86 * q^36 - 7 * q^37 - 12 * q^38 - 14 * q^42 - 14 * q^45 - 8 * q^47 - 20 * q^48 + 94 * q^49 - 12 * q^53 - 22 * q^56 - 18 * q^58 - 11 * q^59 - 26 * q^60 + 80 * q^64 - 13 * q^67 - 19 * q^69 - 24 * q^70 - 15 * q^71 - 18 * q^75 - 30 * q^78 - 28 * q^80 + 84 * q^81 - 22 * q^82 - 24 * q^86 - 13 * q^89 + 64 * q^91 - 30 * q^92 + 61 * q^93 + 67 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1331))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		11
1331.2.a.a	$1331$	$2$	1331.a	1.a	$1$	$5$	$5$	$10.628$	\(\Q(\zeta_{22})^+\)	\(\Q(\sqrt{-11}) \)	✓	✓			1331.2.a.a	$2$	$1$	\(0\)	\(-5\)	\(-4\)	\(0\)		$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q+(-1-\beta _{2}+\beta _{4})q^{3}-2q^{4}+(-2+\cdots)q^{5}+\cdots\)
1331.2.a.b	$1331$	$2$	1331.a	1.a	$1$	$5$	$5$	$10.628$	\(\Q(\zeta_{22})^+\)	\(\Q(\sqrt{-11}) \)	✓	✓			1331.2.a.b	$2$	$0$	\(0\)	\(6\)	\(7\)	\(0\)		$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q+(2+\beta _{2}-2\beta _{3}+\beta _{4})q^{3}-2q^{4}+(1+\cdots)q^{5}+\cdots\)
1331.2.a.c	$1331$	$2$	1331.a	1.a	$1$	$10$	$10$	$10.628$	10.10.\(\cdots\).1	None	✓	✓			1331.2.a.c	$2$	$1$	\(0\)	\(-2\)	\(-12\)	\(0\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
1331.2.a.d	$1331$	$2$	1331.a	1.a	$1$	$25$	$25$	$10.628$		None	✓	✓	✓		1331.2.a.d	$1$	$1$	\(-5\)	\(-3\)	\(-3\)	\(-19\)		$+$	$+$		$\mathrm{SU}(2)$
1331.2.a.e	$1331$	$2$	1331.a	1.a	$1$	$25$	$25$	$10.628$		None	✓	✓			1331.2.a.d	$1$	$0$	\(5\)	\(-3\)	\(-3\)	\(19\)		$-$	$-$		$\mathrm{SU}(2)$
1331.2.a.f	$1331$	$2$	1331.a	1.a	$1$	$30$	$30$	$10.628$		None	✓	✓	✓		1331.2.a.f	$2$	$0$	\(0\)	\(6\)	\(14\)	\(0\)		$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1331))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1331)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 2}\)