Space of modular forms of level 25, weight 4, and trivial character

• Label: 25.4.a
• Level: $25$
• Weight: $4$
• Character orbit: 25.a
• Rep. character: $\chi_{25}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $3$
• Sturm bound: $10$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(10\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(25))\).

	Total	New	Old
Modular forms	11	6	5
Cusp forms	5	3	2
Eisenstein series	6	3	3

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

\(5\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(6\)	\(3\)	\(3\)		\(3\)	\(2\)	\(1\)		\(3\)	\(1\)	\(2\)
\(-\)		\(5\)	\(3\)	\(2\)		\(2\)	\(1\)	\(1\)		\(3\)	\(2\)	\(1\)

Trace form

3 * q + 4 * q^2 - 2 * q^3 - 6 * q^4 + 6 * q^6 - 6 * q^7 + 21 * q^9 - 54 * q^11 - 16 * q^12 + 38 * q^13 - 12 * q^14 + 18 * q^16 - 26 * q^17 - 92 * q^18 + 30 * q^19 + 96 * q^21 + 128 * q^22 + 78 * q^23 - 210 * q^24 + 96 * q^26 + 100 * q^27 - 48 * q^28 + 270 * q^29 - 24 * q^31 - 256 * q^32 - 64 * q^33 + 78 * q^34 - 492 * q^36 - 266 * q^37 + 400 * q^38 - 468 * q^39 - 384 * q^41 + 48 * q^42 - 442 * q^43 + 858 * q^44 + 636 * q^46 + 514 * q^47 + 128 * q^48 - 921 * q^49 + 1326 * q^51 + 304 * q^52 - 2 * q^53 + 330 * q^54 - 180 * q^56 - 200 * q^57 - 200 * q^58 - 60 * q^59 - 1554 * q^61 - 432 * q^62 + 138 * q^63 - 846 * q^64 - 858 * q^66 - 126 * q^67 - 208 * q^68 + 2112 * q^69 + 1236 * q^71 + 878 * q^73 - 1692 * q^74 + 1290 * q^76 - 192 * q^77 - 304 * q^78 + 1620 * q^79 - 1257 * q^81 + 88 * q^82 - 282 * q^83 - 492 * q^84 - 1584 * q^86 + 100 * q^87 - 2040 * q^89 - 564 * q^91 + 624 * q^92 + 216 * q^93 + 2448 * q^94 + 2766 * q^96 - 386 * q^97 - 1228 * q^98 - 2628 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(25))\) 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
25.4.a.a	$25$	$4$	25.a	1.a	$1$	$1$	$1$	$1.475$	\(\Q\)	None	✓	✓	✓	✓	25.4.a.a	$1$	$1$	\(-1\)	\(-7\)	\(0\)	\(-6\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-7q^{3}-7q^{4}+7q^{6}-6q^{7}+\cdots\)
25.4.a.b	$25$	$4$	25.a	1.a	$1$	$1$	$1$	$1.475$	\(\Q\)	None	✓	✓			25.4.a.a	$1$	$0$	\(1\)	\(7\)	\(0\)	\(6\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+7q^{3}-7q^{4}+7q^{6}+6q^{7}+\cdots\)
25.4.a.c	$25$	$4$	25.a	1.a	$1$	$1$	$1$	$1.475$	\(\Q\)	None	✓				5.4.a.a	$1$	$0$	\(4\)	\(-2\)	\(0\)	\(-6\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}-2q^{3}+8q^{4}-8q^{6}-6q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(25))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(25)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)