Space of modular forms of level 4925, weight 2, and trivial character

• Label: 4925.2.a
• Level: $4925$
• Weight: $2$
• Character orbit: 4925.a
• Rep. character: $\chi_{4925}(1,\cdot)$
• Character field: $\Q$
• Dimension: $311$
• Newform subspaces: $19$
• Sturm bound: $990$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 4925 = 5^{2} \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4925.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 19 \)
Sturm bound:			\(990\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4925))\).

	Total	New	Old
Modular forms	500	311	189
Cusp forms	489	311	178
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.

\(5\)	\(197\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(66\)
\(+\)	\(-\)	\(-\)	\(81\)
\(-\)	\(+\)	\(-\)	\(87\)
\(-\)	\(-\)	\(+\)	\(77\)
Plus space		\(+\)	\(143\)
Minus space		\(-\)	\(168\)

Trace form

311 * q + q^2 + 2 * q^3 + 313 * q^4 - 2 * q^6 + 6 * q^7 - 3 * q^8 + 309 * q^9 - 6 * q^11 + 4 * q^12 + 12 * q^13 - 10 * q^14 + 317 * q^16 + 16 * q^17 - 9 * q^18 + 22 * q^19 + 4 * q^22 - 12 * q^23 - 24 * q^24 - 8 * q^26 + 2 * q^27 + 20 * q^28 - 18 * q^29 - 25 * q^32 + 20 * q^33 - 6 * q^34 + 263 * q^36 - 12 * q^38 - 18 * q^39 + 14 * q^42 + 22 * q^43 - 28 * q^44 - 26 * q^46 - 30 * q^47 + 16 * q^48 + 321 * q^49 - 6 * q^51 + 24 * q^52 - 20 * q^53 + 6 * q^54 - 60 * q^56 + 12 * q^57 - 4 * q^58 + 26 * q^59 + 24 * q^61 + 6 * q^62 + 26 * q^63 + 319 * q^64 + 2 * q^66 - 4 * q^67 + 58 * q^68 + 12 * q^69 - 2 * q^71 - 15 * q^72 + 36 * q^73 - 54 * q^74 + 34 * q^76 + 56 * q^77 + 34 * q^78 + 2 * q^79 + 311 * q^81 + 6 * q^82 - 4 * q^83 - 14 * q^84 + 6 * q^86 - 20 * q^87 + 48 * q^88 - 2 * q^89 + 60 * q^91 - 96 * q^92 - 2 * q^93 - 28 * q^94 - 72 * q^96 + 44 * q^97 + 21 * q^98 - 6 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4925))\) 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	197
4925.2.a.a	$4925$	$2$	4925.a	1.a	$1$	$1$	$1$	$39.326$	\(\Q\)	None	✓	✓			4925.2.a.a	$1$	$0$	\(-1\)	\(-1\)	\(0\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}+q^{6}+2q^{7}+3q^{8}+\cdots\)
4925.2.a.b	$4925$	$2$	4925.a	1.a	$1$	$1$	$1$	$39.326$	\(\Q\)	None	✓				985.2.a.b	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-3q^{7}+3q^{8}-3q^{9}+4q^{11}+\cdots\)
4925.2.a.c	$4925$	$2$	4925.a	1.a	$1$	$1$	$1$	$39.326$	\(\Q\)	None	✓	✓			4925.2.a.a	$1$	$0$	\(1\)	\(1\)	\(0\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}+q^{6}-2q^{7}-3q^{8}+\cdots\)
4925.2.a.d	$4925$	$2$	4925.a	1.a	$1$	$1$	$1$	$39.326$	\(\Q\)	None	✓				197.2.a.a	$1$	$0$	\(2\)	\(0\)	\(0\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+3q^{7}-3q^{9}+4q^{11}+\cdots\)
4925.2.a.e	$4925$	$2$	4925.a	1.a	$1$	$1$	$1$	$39.326$	\(\Q\)	None	✓				985.2.a.a	$1$	$1$	\(2\)	\(2\)	\(0\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{3}+2q^{4}+4q^{6}-q^{7}+\cdots\)
4925.2.a.f	$4925$	$2$	4925.a	1.a	$1$	$2$	$2$	$39.326$	\(\Q(\sqrt{17}) \)	None	✓				985.2.a.d	$1$	$0$	\(1\)	\(0\)	\(0\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(2+\beta )q^{4}+(1+\beta )q^{7}+(4+\beta )q^{8}+\cdots\)
4925.2.a.g	$4925$	$2$	4925.a	1.a	$1$	$2$	$2$	$39.326$	\(\Q(\sqrt{2}) \)	None	✓				985.2.a.c	$1$	$0$	\(2\)	\(0\)	\(0\)	\(-6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-2\beta q^{3}-q^{4}-2\beta q^{6}+(-3+\cdots)q^{7}+\cdots\)
4925.2.a.h	$4925$	$2$	4925.a	1.a	$1$	$5$	$5$	$39.326$	5.5.24217.1	None	✓				197.2.a.b	$1$	$0$	\(0\)	\(8\)	\(0\)	\(10\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{2})q^{2}+(2-\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots\)
4925.2.a.i	$4925$	$2$	4925.a	1.a	$1$	$10$	$10$	$39.326$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				197.2.a.c	$1$	$1$	\(0\)	\(-10\)	\(0\)	\(-11\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4925.2.a.j	$4925$	$2$	4925.a	1.a	$1$	$10$	$10$	$39.326$	10.10.\(\cdots\).1	None	✓				985.2.a.e	$1$	$1$	\(2\)	\(3\)	\(0\)	\(6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
4925.2.a.k	$4925$	$2$	4925.a	1.a	$1$	$14$	$14$	$39.326$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓				985.2.a.f	$1$	$0$	\(6\)	\(7\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{8})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
4925.2.a.l	$4925$	$2$	4925.a	1.a	$1$	$17$	$17$	$39.326$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓				985.2.a.g	$1$	$1$	\(-6\)	\(-5\)	\(0\)	\(-7\)		$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
4925.2.a.m	$4925$	$2$	4925.a	1.a	$1$	$18$	$18$	$39.326$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓				985.2.a.h	$1$	$0$	\(-7\)	\(-3\)	\(0\)	\(8\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{8}q^{3}+(2+\beta _{2})q^{4}+(\beta _{7}+\cdots)q^{6}+\cdots\)
4925.2.a.n	$4925$	$2$	4925.a	1.a	$1$	$28$	$28$	$39.326$		None	✓	✓			4925.2.a.n	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
4925.2.a.o	$4925$	$2$	4925.a	1.a	$1$	$28$	$28$	$39.326$		None	✓	✓	✓		4925.2.a.n	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
4925.2.a.p	$4925$	$2$	4925.a	1.a	$1$	$37$	$37$	$39.326$		None	✓	✓			4925.2.a.p	$1$	$0$	\(-2\)	\(-1\)	\(0\)	\(4\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
4925.2.a.q	$4925$	$2$	4925.a	1.a	$1$	$37$	$37$	$39.326$		None	✓	✓	✓		4925.2.a.p	$1$	$0$	\(2\)	\(1\)	\(0\)	\(-4\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
4925.2.a.r	$4925$	$2$	4925.a	1.a	$1$	$49$	$49$	$39.326$		None	✓		✓		985.2.b.a	$1$	$1$	\(-5\)	\(-22\)	\(0\)	\(-32\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
4925.2.a.s	$4925$	$2$	4925.a	1.a	$1$	$49$	$49$	$39.326$		None	✓		✓		985.2.b.a	$1$	$0$	\(5\)	\(22\)	\(0\)	\(32\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4925))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4925)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(197))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(985))\)\(^{\oplus 2}\)