Space of modular forms of level 6275, weight 2, and trivial character

• Label: 6275.2.a
• Level: $6275$
• Weight: $2$
• Character orbit: 6275.a
• Rep. character: $\chi_{6275}(1,\cdot)$
• Character field: $\Q$
• Dimension: $396$
• Newform subspaces: $14$
• Sturm bound: $1260$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 6275 = 5^{2} \cdot 251 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6275.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(1260\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6275))\).

	Total	New	Old
Modular forms	636	396	240
Cusp forms	625	396	229
Eisenstein series	11	0	11

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

\(5\)	\(251\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(87\)
\(+\)	\(-\)	$-$	\(101\)
\(-\)	\(+\)	$-$	\(118\)
\(-\)	\(-\)	$+$	\(90\)
Plus space		\(+\)	\(177\)
Minus space		\(-\)	\(219\)

Trace form

\( 396 q + q^{2} + 2 q^{3} + 395 q^{4} - 2 q^{6} + 8 q^{7} + 3 q^{8} + 388 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6275))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	251
6275.2.a.a	$6275$	$2$	6275.a	1.a	$1$	$2$	$2$	$50.106$	\(\Q(\sqrt{5}) \)	None	✓		1255.2.a.a	$1$	$1$	\(-3\)	\(-2\)	\(0\)	\(4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(1+\beta )q^{6}+\cdots\)
6275.2.a.b	$6275$	$2$	6275.a	1.a	$1$	$4$	$4$	$50.106$	4.4.2225.1	None	✓		1255.2.a.b	$1$	$1$	\(2\)	\(-2\)	\(0\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(-1-\beta _{3})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
6275.2.a.c	$6275$	$2$	6275.a	1.a	$1$	$4$	$4$	$50.106$	4.4.725.1	None	✓		251.2.a.a	$1$	$1$	\(2\)	\(2\)	\(0\)	\(3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{2}+\beta _{2}q^{3}-\beta _{3}q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
6275.2.a.d	$6275$	$2$	6275.a	1.a	$1$	$14$	$14$	$50.106$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓		1255.2.a.c	$1$	$1$	\(1\)	\(3\)	\(0\)	\(3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{10}q^{3}+(1+\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
6275.2.a.e	$6275$	$2$	6275.a	1.a	$1$	$17$	$17$	$50.106$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓		251.2.a.b	$1$	$0$	\(-2\)	\(0\)	\(0\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{3}+\cdots)q^{6}+\cdots\)
6275.2.a.f	$6275$	$2$	6275.a	1.a	$1$	$18$	$18$	$50.106$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓		1255.2.a.d	$1$	$0$	\(9\)	\(7\)	\(0\)	\(13\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}-\beta _{7}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
6275.2.a.g	$6275$	$2$	6275.a	1.a	$1$	$21$	$21$	$50.106$		None	✓		1255.2.a.e	$1$	$1$	\(-5\)	\(-3\)	\(0\)	\(-11\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
6275.2.a.h	$6275$	$2$	6275.a	1.a	$1$	$24$	$24$	$50.106$		None	✓		1255.2.a.f	$1$	$0$	\(-3\)	\(-3\)	\(0\)	\(1\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
6275.2.a.i	$6275$	$2$	6275.a	1.a	$1$	$42$	$42$	$50.106$		None	✓	✓	6275.2.a.i	$1$	$1$	\(-8\)	\(-5\)	\(0\)	\(-14\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
6275.2.a.j	$6275$	$2$	6275.a	1.a	$1$	$42$	$42$	$50.106$		None	✓	✓	6275.2.a.j	$1$	$1$	\(-6\)	\(-7\)	\(0\)	\(-14\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
6275.2.a.k	$6275$	$2$	6275.a	1.a	$1$	$42$	$42$	$50.106$		None	✓	✓	6275.2.a.j	$1$	$0$	\(6\)	\(7\)	\(0\)	\(14\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
6275.2.a.l	$6275$	$2$	6275.a	1.a	$1$	$42$	$42$	$50.106$		None	✓	✓	6275.2.a.i	$1$	$0$	\(8\)	\(5\)	\(0\)	\(14\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
6275.2.a.m	$6275$	$2$	6275.a	1.a	$1$	$48$	$48$	$50.106$		None	✓		1255.2.b.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
6275.2.a.n	$6275$	$2$	6275.a	1.a	$1$	$76$	$76$	$50.106$		None	✓		1255.2.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6275))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6275)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(251))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1255))\)\(^{\oplus 2}\)