Space of modular forms of level 925, weight 2, and trivial character

• Label: 925.2.a
• Level: $925$
• Weight: $2$
• Character orbit: 925.a
• Rep. character: $\chi_{925}(1,\cdot)$
• Character field: $\Q$
• Dimension: $57$
• Newform subspaces: $13$
• Sturm bound: $190$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(190\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(925))\).

	Total	New	Old
Modular forms	100	57	43
Cusp forms	89	57	32
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.

\(5\)	\(37\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(23\)	\(12\)	\(11\)		\(21\)	\(12\)	\(9\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)		\(26\)	\(15\)	\(11\)		\(23\)	\(15\)	\(8\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)		\(27\)	\(16\)	\(11\)		\(24\)	\(16\)	\(8\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)		\(24\)	\(14\)	\(10\)		\(21\)	\(14\)	\(7\)		\(3\)	\(0\)	\(3\)
Plus space		\(+\)		\(47\)	\(26\)	\(21\)		\(42\)	\(26\)	\(16\)		\(5\)	\(0\)	\(5\)
Minus space		\(-\)		\(53\)	\(31\)	\(22\)		\(47\)	\(31\)	\(16\)		\(6\)	\(0\)	\(6\)

Trace form

57 * q + q^2 + 2 * q^3 + 53 * q^4 - 2 * q^6 - 6 * q^7 + 3 * q^8 + 55 * q^9 - 2 * q^11 + 4 * q^12 - 18 * q^14 + 29 * q^16 + 8 * q^17 + 11 * q^18 - 10 * q^19 - 18 * q^21 + 2 * q^22 - 8 * q^23 + 10 * q^26 + 14 * q^27 - 12 * q^28 - 22 * q^29 - 12 * q^31 - 13 * q^32 - 10 * q^33 - 18 * q^34 + 33 * q^36 + q^37 + 24 * q^38 - 34 * q^39 + 16 * q^41 + 42 * q^42 - 14 * q^43 + 4 * q^44 + 4 * q^46 - 6 * q^47 + 40 * q^48 + 31 * q^49 - 2 * q^51 + 18 * q^52 + 24 * q^53 - 6 * q^54 - 36 * q^56 + 2 * q^57 + 30 * q^58 + 28 * q^59 - 18 * q^61 - 36 * q^62 - 64 * q^63 + 9 * q^64 + 34 * q^66 - 24 * q^67 - 2 * q^68 - 20 * q^69 - 26 * q^71 - 13 * q^72 - 8 * q^73 - 5 * q^74 - 68 * q^76 + 22 * q^77 - 64 * q^78 - 50 * q^79 + 25 * q^81 - 4 * q^82 - 38 * q^83 - 92 * q^84 - 60 * q^86 + 20 * q^88 - 36 * q^89 - 26 * q^91 - 56 * q^92 + 20 * q^93 + 50 * q^94 + 56 * q^96 + 6 * q^97 + 15 * q^98 + 28 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(925))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	37
925.2.a.a	$925$	$2$	925.a	1.a	$1$	$1$	$1$	$7.386$	\(\Q\)	None	✓				185.2.a.c	$1$	$0$	\(-1\)	\(2\)	\(0\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}-q^{4}-2q^{6}+2q^{7}+3q^{8}+\cdots\)
925.2.a.b	$925$	$2$	925.a	1.a	$1$	$1$	$1$	$7.386$	\(\Q\)	None	✓				37.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}+q^{7}-2q^{9}+3q^{11}+\cdots\)
925.2.a.c	$925$	$2$	925.a	1.a	$1$	$1$	$1$	$7.386$	\(\Q\)	None	✓				185.2.a.b	$1$	$1$	\(0\)	\(1\)	\(0\)	\(3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+3q^{7}-2q^{9}-5q^{11}+\cdots\)
925.2.a.d	$925$	$2$	925.a	1.a	$1$	$1$	$1$	$7.386$	\(\Q\)	None	✓				185.2.a.a	$1$	$0$	\(2\)	\(-1\)	\(0\)	\(5\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-q^{3}+2q^{4}-2q^{6}+5q^{7}+\cdots\)
925.2.a.e	$925$	$2$	925.a	1.a	$1$	$1$	$1$	$7.386$	\(\Q\)	None	✓				37.2.a.a	$1$	$0$	\(2\)	\(3\)	\(0\)	\(1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+3q^{3}+2q^{4}+6q^{6}+q^{7}+\cdots\)
925.2.a.f	$925$	$2$	925.a	1.a	$1$	$5$	$5$	$7.386$	5.5.973904.1	None	✓				185.2.a.e	$1$	$1$	\(-2\)	\(-3\)	\(0\)	\(-11\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{2}+(-1+\beta _{1})q^{3}+(2+\beta _{3})q^{4}+\cdots\)
925.2.a.g	$925$	$2$	925.a	1.a	$1$	$5$	$5$	$7.386$	5.5.65657.1	None	✓	✓			925.2.a.g	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}-\beta _{3}q^{3}+\beta _{1}q^{4}+(-1+\beta _{3}+\cdots)q^{6}+\cdots\)
925.2.a.h	$925$	$2$	925.a	1.a	$1$	$5$	$5$	$7.386$	5.5.368464.1	None	✓				185.2.a.d	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-7\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+\beta _{3}q^{3}+(2-\beta _{1}-\beta _{4})q^{4}+\cdots\)
925.2.a.i	$925$	$2$	925.a	1.a	$1$	$5$	$5$	$7.386$	5.5.65657.1	None	✓	✓			925.2.a.g	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+\beta _{3}q^{3}+\beta _{1}q^{4}+(-1+\beta _{3}+\cdots)q^{6}+\cdots\)
925.2.a.j	$925$	$2$	925.a	1.a	$1$	$7$	$7$	$7.386$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			925.2.a.j	$1$	$0$	\(-1\)	\(1\)	\(0\)	\(0\)		$-$	$+$	$-$	$3$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{6}+\cdots\)
925.2.a.k	$925$	$2$	925.a	1.a	$1$	$7$	$7$	$7.386$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓		925.2.a.j	$1$	$0$	\(1\)	\(-1\)	\(0\)	\(0\)		$+$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{6}+\cdots\)
925.2.a.l	$925$	$2$	925.a	1.a	$1$	$9$	$9$	$7.386$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		185.2.b.a	$1$	$1$	\(-5\)	\(-8\)	\(0\)	\(-8\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-1+\beta _{6})q^{3}+(2+\cdots)q^{4}+\cdots\)
925.2.a.m	$925$	$2$	925.a	1.a	$1$	$9$	$9$	$7.386$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		185.2.b.a	$1$	$0$	\(5\)	\(8\)	\(0\)	\(8\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-\beta _{6})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(925))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(925)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(185))\)\(^{\oplus 2}\)