Space of modular forms of level 25, weight 6, and trivial character

• Label: 25.6.a
• Level: $25$
• Weight: $6$
• Character orbit: 25.a
• Rep. character: $\chi_{25}(1,\cdot)$
• Character field: $\Q$
• Dimension: $7$
• Newform subspaces: $4$
• Sturm bound: $15$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(15\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(25))\).

	Total	New	Old
Modular forms	15	10	5
Cusp forms	9	7	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
\(+\)		\(7\)	\(4\)	\(3\)		\(4\)	\(3\)	\(1\)		\(3\)	\(1\)	\(2\)
\(-\)		\(8\)	\(6\)	\(2\)		\(5\)	\(4\)	\(1\)		\(3\)	\(2\)	\(1\)

Trace form

7 * q - 2 * q^2 + 4 * q^3 + 134 * q^4 - 126 * q^6 - 192 * q^7 + 120 * q^8 + 471 * q^9 - 36 * q^11 - 112 * q^12 - 286 * q^13 - 372 * q^14 + 402 * q^16 + 1678 * q^17 + 454 * q^18 - 4860 * q^19 + 2784 * q^21 + 296 * q^22 - 2976 * q^23 + 270 * q^24 - 7356 * q^26 - 1880 * q^27 + 5376 * q^28 + 2610 * q^29 + 8864 * q^31 - 5152 * q^32 - 592 * q^33 + 27718 * q^34 - 24648 * q^36 - 182 * q^37 - 2120 * q^38 + 11832 * q^39 + 45714 * q^41 + 1536 * q^42 + 1244 * q^43 - 63582 * q^44 - 21436 * q^46 + 12088 * q^47 + 2624 * q^48 - 29801 * q^49 - 56496 * q^51 + 8008 * q^52 - 23846 * q^53 - 12810 * q^54 + 101340 * q^56 + 4240 * q^57 + 6820 * q^58 + 53220 * q^59 - 27886 * q^61 + 4896 * q^62 + 43584 * q^63 + 102594 * q^64 + 44898 * q^66 - 60972 * q^67 - 46984 * q^68 - 71808 * q^69 - 100536 * q^71 - 27240 * q^72 + 38774 * q^73 + 103248 * q^74 - 159470 * q^76 + 28416 * q^77 + 2288 * q^78 - 6240 * q^79 - 5433 * q^81 + 18796 * q^82 - 16716 * q^83 - 91692 * q^84 + 500904 * q^86 - 13640 * q^87 - 17760 * q^88 - 24270 * q^89 - 496 * q^91 + 83328 * q^92 - 9792 * q^93 - 407312 * q^94 - 341826 * q^96 + 119038 * q^97 - 40114 * q^98 + 554292 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(25))\) 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
25.6.a.a	$25$	$6$	25.a	1.a	$1$	$1$	$1$	$4.010$	\(\Q\)	None	✓				5.6.a.a	$1$	$1$	\(-2\)	\(4\)	\(0\)	\(-192\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+4q^{3}-28q^{4}-8q^{6}-192q^{7}+\cdots\)
25.6.a.b	$25$	$6$	25.a	1.a	$1$	$2$	$2$	$4.010$	\(\Q(\sqrt{241}) \)	None	✓	✓	✓		25.6.a.b	$1$	$1$	\(-5\)	\(-20\)	\(0\)	\(-200\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-2-\beta )q^{2}+(-11+2\beta )q^{3}+(2^{5}+\cdots)q^{4}+\cdots\)
25.6.a.c	$25$	$6$	25.a	1.a	$1$	$2$	$2$	$4.010$	\(\Q(\sqrt{11}) \)	None	✓				5.6.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+3\beta q^{3}+12q^{4}+132q^{6}+\cdots\)
25.6.a.d	$25$	$6$	25.a	1.a	$1$	$2$	$2$	$4.010$	\(\Q(\sqrt{241}) \)	None	✓	✓			25.6.a.b	$1$	$0$	\(5\)	\(20\)	\(0\)	\(200\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(3-\beta )q^{2}+(9+2\beta )q^{3}+(37-5\beta )q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(25))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(25)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)