Space of modular forms of level 6025, weight 2, and trivial character

• Label: 6025.2.a
• Level: $6025$
• Weight: $2$
• Character orbit: 6025.a
• Rep. character: $\chi_{6025}(1,\cdot)$
• Character field: $\Q$
• Dimension: $380$
• Newform subspaces: $17$
• Sturm bound: $1210$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(1210\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6025))\).

	Total	New	Old
Modular forms	610	380	230
Cusp forms	599	380	219
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.

\(5\)	\(241\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(87\)
\(+\)	\(-\)	$-$	\(93\)
\(-\)	\(+\)	$-$	\(106\)
\(-\)	\(-\)	$+$	\(94\)
Plus space		\(+\)	\(181\)
Minus space		\(-\)	\(199\)

Trace form

\( 380 q + 2 q^{2} - 2 q^{3} + 382 q^{4} + 6 q^{6} + 6 q^{8} + 374 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6025))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	241
6025.2.a.a	$6025$	$2$	6025.a	1.a	$1$	$2$	$2$	$48.110$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-2\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta q^{3}-q^{4}-\beta q^{6}+(-2+2\beta )q^{7}+\cdots\)
6025.2.a.b	$6025$	$2$	6025.a	1.a	$1$	$2$	$2$	$48.110$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-2\beta )q^{2}+(-2+\beta )q^{3}+3q^{4}+\cdots\)
6025.2.a.c	$6025$	$2$	6025.a	1.a	$1$	$2$	$2$	$48.110$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(3\)	\(0\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-2\beta )q^{2}+(1+\beta )q^{3}+3q^{4}+(-1+\cdots)q^{6}+\cdots\)
6025.2.a.d	$6025$	$2$	6025.a	1.a	$1$	$2$	$2$	$48.110$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(2\)	\(-1\)	\(0\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta )q^{3}-q^{4}+(-1+\beta )q^{6}+\cdots\)
6025.2.a.e	$6025$	$2$	6025.a	1.a	$1$	$5$	$5$	$48.110$	5.5.38569.1	None	✓	$1$	$0$	\(1\)	\(5\)	\(0\)	\(10\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{3})q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{4})q^{3}+\cdots\)
6025.2.a.f	$6025$	$2$	6025.a	1.a	$1$	$7$	$7$	$48.110$	7.7.31056073.1	None	✓	$1$	$1$	\(4\)	\(3\)	\(0\)	\(7\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}-\beta _{6}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
6025.2.a.g	$6025$	$2$	6025.a	1.a	$1$	$11$	$11$	$48.110$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(8\)	\(0\)	\(9\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}+\beta _{2})q^{2}+(1+\beta _{2}+\beta _{3})q^{3}+\cdots\)
6025.2.a.h	$6025$	$2$	6025.a	1.a	$1$	$12$	$12$	$48.110$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(-3\)	\(-1\)	\(0\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{3}+\cdots)q^{6}+\cdots\)
6025.2.a.i	$6025$	$2$	6025.a	1.a	$1$	$15$	$15$	$48.110$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$1$	\(-2\)	\(7\)	\(0\)	\(3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{11}q^{3}+\beta _{2}q^{4}+(-\beta _{8}+\cdots)q^{6}+\cdots\)
6025.2.a.j	$6025$	$2$	6025.a	1.a	$1$	$25$	$25$	$48.110$		None	✓	$1$	$1$	\(-6\)	\(-15\)	\(0\)	\(-19\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
6025.2.a.k	$6025$	$2$	6025.a	1.a	$1$	$25$	$25$	$48.110$		None	✓	$1$	$0$	\(4\)	\(-9\)	\(0\)	\(-7\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
6025.2.a.l	$6025$	$2$	6025.a	1.a	$1$	$40$	$40$	$48.110$		None	✓	$1$	$1$	\(-11\)	\(-8\)	\(0\)	\(-16\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
6025.2.a.m	$6025$	$2$	6025.a	1.a	$1$	$40$	$40$	$48.110$		None	✓	$1$	$1$	\(-9\)	\(-8\)	\(0\)	\(-20\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
6025.2.a.n	$6025$	$2$	6025.a	1.a	$1$	$40$	$40$	$48.110$		None	✓	$1$	$0$	\(9\)	\(8\)	\(0\)	\(20\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
6025.2.a.o	$6025$	$2$	6025.a	1.a	$1$	$40$	$40$	$48.110$		None	✓	$1$	$0$	\(11\)	\(8\)	\(0\)	\(16\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
6025.2.a.p	$6025$	$2$	6025.a	1.a	$1$	$46$	$46$	$48.110$		None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
6025.2.a.q	$6025$	$2$	6025.a	1.a	$1$	$66$	$66$	$48.110$		None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6025))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6025)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(241))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1205))\)\(^{\oplus 2}\)