Space of modular forms of level 7381, weight 2, and trivial character

• Label: 7381.2.a
• Level: $7381$
• Weight: $2$
• Character orbit: 7381.a
• Rep. character: $\chi_{7381}(1,\cdot)$
• Character field: $\Q$
• Dimension: $545$
• Newform subspaces: $22$
• Sturm bound: $1364$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 7381 = 11^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7381.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 22 \)
Sturm bound:			\(1364\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7381))\).

	Total	New	Old
Modular forms	694	545	149
Cusp forms	671	545	126
Eisenstein series	23	0	23

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

\(11\)	\(61\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(129\)
\(+\)	\(-\)	$-$	\(141\)
\(-\)	\(+\)	$-$	\(145\)
\(-\)	\(-\)	$+$	\(130\)
Plus space		\(+\)	\(259\)
Minus space		\(-\)	\(286\)

Trace form

\( 545 q - 3 q^{2} - 4 q^{3} + 543 q^{4} - 2 q^{5} + 2 q^{6} - 6 q^{7} + 3 q^{8} + 533 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7381))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		11	61
7381.2.a.a	$7381$	$2$	7381.a	1.a	$1$	$1$	$1$	$58.938$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+3q^{5}-2q^{7}-2q^{9}+\cdots\)
7381.2.a.b	$7381$	$2$	7381.a	1.a	$1$	$1$	$1$	$58.938$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(3\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+3q^{5}+2q^{7}-2q^{9}+\cdots\)
7381.2.a.c	$7381$	$2$	7381.a	1.a	$1$	$1$	$1$	$58.938$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-2\)	\(-3\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2q^{3}-q^{4}-3q^{5}-2q^{6}-q^{7}+\cdots\)
7381.2.a.d	$7381$	$2$	7381.a	1.a	$1$	$2$	$2$	$58.938$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$2$	\(-4\)	\(-2\)	\(-3\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(-2+2\beta )q^{3}+2q^{4}+(-2+\cdots)q^{5}+\cdots\)
7381.2.a.e	$7381$	$2$	7381.a	1.a	$1$	$2$	$2$	$58.938$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(4\)	\(-2\)	\(-3\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-2+2\beta )q^{3}+2q^{4}+(-2+\cdots)q^{5}+\cdots\)
7381.2.a.f	$7381$	$2$	7381.a	1.a	$1$	$3$	$3$	$58.938$	3.3.148.1	None	✓	$1$	$0$	\(-1\)	\(2\)	\(-1\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
7381.2.a.g	$7381$	$2$	7381.a	1.a	$1$	$5$	$5$	$58.938$	5.5.24217.1	None	✓	$1$	$0$	\(2\)	\(0\)	\(-2\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{4})q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
7381.2.a.h	$7381$	$2$	7381.a	1.a	$1$	$6$	$6$	$58.938$	6.6.2661761.1	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}-\beta _{1}q^{3}-\beta _{5}q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
7381.2.a.i	$7381$	$2$	7381.a	1.a	$1$	$19$	$19$	$58.938$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	$1$	$1$	\(-5\)	\(0\)	\(0\)	\(-9\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{11}q^{3}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
7381.2.a.j	$7381$	$2$	7381.a	1.a	$1$	$21$	$21$	$58.938$		None	✓	$1$	$0$	\(0\)	\(3\)	\(7\)	\(-5\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
7381.2.a.k	$7381$	$2$	7381.a	1.a	$1$	$24$	$24$	$58.938$		None	✓	$1$	$1$	\(-5\)	\(-2\)	\(-4\)	\(-6\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
7381.2.a.l	$7381$	$2$	7381.a	1.a	$1$	$24$	$24$	$58.938$		None	✓	$1$	$0$	\(5\)	\(-2\)	\(-4\)	\(6\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
7381.2.a.m	$7381$	$2$	7381.a	1.a	$1$	$25$	$25$	$58.938$		None	✓	$1$	$1$	\(-5\)	\(-1\)	\(-1\)	\(-4\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
7381.2.a.n	$7381$	$2$	7381.a	1.a	$1$	$25$	$25$	$58.938$		None	✓	$1$	$1$	\(-5\)	\(-1\)	\(-1\)	\(-4\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
7381.2.a.o	$7381$	$2$	7381.a	1.a	$1$	$25$	$25$	$58.938$		None	✓	$1$	$0$	\(5\)	\(-1\)	\(-1\)	\(4\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
7381.2.a.p	$7381$	$2$	7381.a	1.a	$1$	$25$	$25$	$58.938$		None	✓	$1$	$0$	\(5\)	\(-1\)	\(-1\)	\(4\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
7381.2.a.q	$7381$	$2$	7381.a	1.a	$1$	$50$	$50$	$58.938$		None	✓	$1$	$1$	\(-10\)	\(-2\)	\(-2\)	\(-8\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
7381.2.a.r	$7381$	$2$	7381.a	1.a	$1$	$50$	$50$	$58.938$		None	✓	$1$	$0$	\(10\)	\(-2\)	\(-2\)	\(8\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
7381.2.a.s	$7381$	$2$	7381.a	1.a	$1$	$54$	$54$	$58.938$		None	✓	$1$	$1$	\(-1\)	\(-15\)	\(-14\)	\(-2\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
7381.2.a.t	$7381$	$2$	7381.a	1.a	$1$	$54$	$54$	$58.938$		None	✓	$1$	$1$	\(1\)	\(-15\)	\(-14\)	\(2\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
7381.2.a.u	$7381$	$2$	7381.a	1.a	$1$	$64$	$64$	$58.938$		None	✓	$1$	$0$	\(-5\)	\(19\)	\(21\)	\(-6\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
7381.2.a.v	$7381$	$2$	7381.a	1.a	$1$	$64$	$64$	$58.938$		None	✓	$1$	$0$	\(5\)	\(19\)	\(21\)	\(6\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7381))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7381)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(61))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(671))\)\(^{\oplus 2}\)