Space of modular forms of level 25, weight 22, and trivial character

• Label: 25.22.a
• Level: $25$
• Weight: $22$
• Character orbit: 25.a
• Rep. character: $\chi_{25}(1,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $6$
• Sturm bound: $55$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(55\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_0(25))\).

	Total	New	Old
Modular forms	55	35	20
Cusp forms	49	32	17
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
\(+\)		\(27\)	\(16\)	\(11\)		\(24\)	\(15\)	\(9\)		\(3\)	\(1\)	\(2\)
\(-\)		\(28\)	\(19\)	\(9\)		\(25\)	\(17\)	\(8\)		\(3\)	\(2\)	\(1\)

Trace form

32 * q - 1310 * q^2 - 6590 * q^3 + 32915734 * q^4 + 32120394 * q^6 - 428951550 * q^7 - 7470710280 * q^8 + 80388051186 * q^9 + 58763249334 * q^11 + 243789580880 * q^12 + 23264691220 * q^13 - 506951114052 * q^14 + 32112566276562 * q^16 - 3785812896680 * q^17 - 79878729601190 * q^18 - 24154696946670 * q^19 + 182223686292744 * q^21 + 175723908487480 * q^22 - 314700067836570 * q^23 - 67037684537010 * q^24 + 2014979553112524 * q^26 + 1055133403919020 * q^27 - 1299171721121280 * q^28 + 4820308939119420 * q^29 - 5585445646540376 * q^31 - 2420800928707360 * q^32 + 35220308652025520 * q^33 - 8284606831073002 * q^34 + 6980250692091432 * q^36 - 49064421428406340 * q^37 - 40457968300985720 * q^38 + 127347070012212372 * q^39 + 261437066428652094 * q^41 + 362988657678789120 * q^42 - 201505254636709550 * q^43 - 179301115045948542 * q^44 - 60161303411641196 * q^46 - 194004714502145870 * q^47 + 308249523197103680 * q^48 + 1270188082523538524 * q^49 + 1415488094879008494 * q^51 - 1873978492365746200 * q^52 + 494105394664988260 * q^53 + 2792566678962993630 * q^54 - 1110996081424157220 * q^56 - 7087781283410679560 * q^57 + 12873215227165950620 * q^58 + 7953250308224170440 * q^59 - 11953639026389589116 * q^61 - 27985731899308528320 * q^62 - 4251178160982943710 * q^63 + 35523556004777871234 * q^64 + 34000825488469728378 * q^66 - 27434750902485096330 * q^67 - 2901526404081532840 * q^68 + 57893355838380787512 * q^69 + 3521670663441710604 * q^71 - 280723812246152312040 * q^72 + 77387927225337815080 * q^73 + 271638942795379469448 * q^74 - 156453492294789262990 * q^76 - 465454454501233790400 * q^77 + 455904321870956375600 * q^78 + 476055374305712350020 * q^79 + 93560094364982400732 * q^81 - 793438364204538301420 * q^82 + 275334409479725858490 * q^83 + 1513753550869256027028 * q^84 + 416866803375602317464 * q^86 - 1559745135897410874740 * q^87 + 736206990879619028640 * q^88 + 2404945959225835938510 * q^89 + 928037267440372207324 * q^91 - 3607084121648970468480 * q^92 + 675459022106427394920 * q^93 + 2386779789781437900848 * q^94 + 1191732516861701720574 * q^96 - 1991400758443910752720 * q^97 + 1036011348253477262930 * q^98 + 4090869190521055886832 * q^99

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(25))\) 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
25.22.a.a	$25$	$22$	25.a	1.a	$1$	$1$	$1$	$69.869$	\(\Q\)	None	✓				1.22.a.a	$1$	$1$	\(288\)	\(128844\)	\(0\)	\(768078808\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+288q^{2}+128844q^{3}-2014208q^{4}+\cdots\)
25.22.a.b	$25$	$22$	25.a	1.a	$1$	$3$	$3$	$69.869$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓				5.22.a.a	$1$	$1$	\(1312\)	\(-52194\)	\(0\)	\(-684416558\)		$+$	$+$	$2^{7}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q+(437-\beta _{1})q^{2}+(-17400-8\beta _{1}+\cdots)q^{3}+\cdots\)
25.22.a.c	$25$	$22$	25.a	1.a	$1$	$4$	$4$	$69.869$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				5.22.a.b	$1$	$1$	\(-2910\)	\(-83240\)	\(0\)	\(-512613800\)		$+$	$+$	$2^{6}\cdot 3\cdot 5^{2}\cdot 7$	$\mathrm{SU}(2)$	\(q+(-728+\beta _{1})q^{2}+(-20803-14\beta _{1}+\cdots)q^{3}+\cdots\)
25.22.a.d	$25$	$22$	25.a	1.a	$1$	$7$	$7$	$69.869$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓		25.22.a.d	$1$	$1$	\(-737\)	\(-50381\)	\(0\)	\(-817782442\)		$+$	$+$	$2^{13}\cdot 3^{3}\cdot 5^{10}\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q+(-105-\beta _{1})q^{2}+(-7198+2\beta _{1}+\cdots)q^{3}+\cdots\)
25.22.a.e	$25$	$22$	25.a	1.a	$1$	$7$	$7$	$69.869$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			25.22.a.d	$1$	$0$	\(737\)	\(50381\)	\(0\)	\(817782442\)		$-$	$-$	$2^{13}\cdot 3^{3}\cdot 5^{10}\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q+(105+\beta _{1})q^{2}+(7198-2\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
25.22.a.f	$25$	$22$	25.a	1.a	$1$	$10$	$10$	$69.869$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		5.22.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$2^{30}\cdot 3^{10}\cdot 5^{24}\cdot 7^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(6\beta _{1}-\beta _{4})q^{3}+(927372+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_0(25))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_0(25)) \simeq \) \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)