Space of modular forms of level 7569, weight 2, and trivial character

• Label: 7569.2.a
• Level: $7569$
• Weight: $2$
• Character orbit: 7569.a
• Rep. character: $\chi_{7569}(1,\cdot)$
• Character field: $\Q$
• Dimension: $325$
• Newform subspaces: $49$
• Sturm bound: $1740$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 7569 = 3^{2} \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7569.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 49 \)
Sturm bound:			\(1740\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(2\), \(5\), \(7\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7569))\).

	Total	New	Old
Modular forms	930	352	578
Cusp forms	811	325	486
Eisenstein series	119	27	92

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

\(3\)	\(29\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(225\)	\(61\)	\(164\)		\(196\)	\(61\)	\(135\)		\(29\)	\(0\)	\(29\)
\(+\)	\(-\)	\(-\)		\(239\)	\(75\)	\(164\)		\(209\)	\(75\)	\(134\)		\(30\)	\(0\)	\(30\)
\(-\)	\(+\)	\(-\)		\(240\)	\(111\)	\(129\)		\(210\)	\(98\)	\(112\)		\(30\)	\(13\)	\(17\)
\(-\)	\(-\)	\(+\)		\(226\)	\(105\)	\(121\)		\(196\)	\(91\)	\(105\)		\(30\)	\(14\)	\(16\)
Plus space		\(+\)		\(451\)	\(166\)	\(285\)		\(392\)	\(152\)	\(240\)		\(59\)	\(14\)	\(45\)
Minus space		\(-\)		\(479\)	\(186\)	\(293\)		\(419\)	\(173\)	\(246\)		\(60\)	\(13\)	\(47\)

Trace form

325 * q + q^2 + 317 * q^4 - 3 * q^8 + 4 * q^10 - 2 * q^11 + 4 * q^13 - 4 * q^14 + 301 * q^16 + 6 * q^17 - 24 * q^20 + 273 * q^25 + 8 * q^26 - 10 * q^28 - 6 * q^31 + 5 * q^32 - 28 * q^34 - 4 * q^35 + 10 * q^37 + 2 * q^38 + 16 * q^40 + 10 * q^41 + 2 * q^43 - 14 * q^44 + 12 * q^46 - 14 * q^47 + 257 * q^49 + 53 * q^50 + 22 * q^52 + 24 * q^53 - 14 * q^55 + 32 * q^56 + 14 * q^59 + 14 * q^61 + 12 * q^62 + 239 * q^64 - 4 * q^65 - 18 * q^67 + 38 * q^68 + 8 * q^70 - 36 * q^71 - 10 * q^73 - 8 * q^74 - 24 * q^76 - 8 * q^77 + 2 * q^79 - 22 * q^80 + 28 * q^82 - 14 * q^83 + 24 * q^85 + 36 * q^86 - 50 * q^88 - 6 * q^89 + 20 * q^91 + 50 * q^92 + 22 * q^94 - 44 * q^95 - 34 * q^97 - 11 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7569))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	29
7569.2.a.a	$7569$	$2$	7569.a	1.a	$1$	$1$	$1$	$60.439$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	✓			7569.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}-q^{7}+2q^{13}+4q^{16}-q^{19}+\cdots\)
7569.2.a.b	$7569$	$2$	7569.a	1.a	$1$	$1$	$1$	$60.439$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	✓			7569.2.a.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-1\)		$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}-q^{7}+2q^{13}+4q^{16}+q^{19}+\cdots\)
7569.2.a.c	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	\(\Q(\sqrt{2}) \)	None	✓				29.2.a.a	$1$	$0$	\(-2\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+2\beta q^{7}+\cdots\)
7569.2.a.d	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	\(\Q(\sqrt{5}) \)	None	✓				841.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+(-2+3\beta )q^{5}+\cdots\)
7569.2.a.e	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	\(\Q(\sqrt{5}) \)	None	✓				2523.2.a.b	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+(1-\beta )q^{5}+(2+\cdots)q^{7}+\cdots\)
7569.2.a.f	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	\(\Q(\sqrt{5}) \)	None	✓				87.2.c.a	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+2\beta q^{5}+(-1+\cdots)q^{7}+\cdots\)
7569.2.a.g	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	\(\Q(\sqrt{5}) \)	None	✓				2523.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(3\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+(1+\beta )q^{5}+(-1+\cdots)q^{7}+\cdots\)
7569.2.a.h	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	\(\Q(\sqrt{5}) \)	None	✓				261.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(4\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+2q^{5}+(-1+\cdots)q^{7}+\cdots\)
7569.2.a.i	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	\(\Q(\sqrt{5}) \)	None	✓				29.2.b.a	$2$	$1$	\(0\)	\(0\)	\(-6\)	\(4\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+3q^{4}-3q^{5}+2q^{7}-\beta q^{8}+\cdots\)
7569.2.a.j	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	\(\Q(\sqrt{5}) \)	None	✓				261.2.a.a	$1$	$1$	\(1\)	\(0\)	\(-4\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}-2q^{5}+(-1+\cdots)q^{7}+\cdots\)
7569.2.a.k	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	\(\Q(\sqrt{5}) \)	None	✓				87.2.a.a	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}+(-2+2\beta )q^{5}+\cdots\)
7569.2.a.l	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	\(\Q(\sqrt{5}) \)	None	✓				841.2.a.a	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}+(-2+3\beta )q^{5}+\cdots\)
7569.2.a.m	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	\(\Q(\sqrt{5}) \)	None	✓				2523.2.a.b	$1$	$0$	\(1\)	\(0\)	\(1\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}+(1-\beta )q^{5}+(2+\cdots)q^{7}+\cdots\)
7569.2.a.n	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	\(\Q(\sqrt{5}) \)	None	✓				87.2.c.a	$1$	$1$	\(1\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}+2\beta q^{5}+(-1+\cdots)q^{7}+\cdots\)
7569.2.a.o	$7569$	$2$	7569.a	1.a	$1$	$2$	$2$	$60.439$	\(\Q(\sqrt{5}) \)	None	✓				2523.2.a.a	$1$	$0$	\(1\)	\(0\)	\(3\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}+(1+\beta )q^{5}+(-1+\cdots)q^{7}+\cdots\)
7569.2.a.p	$7569$	$2$	7569.a	1.a	$1$	$3$	$3$	$60.439$	\(\Q(\zeta_{14})^+\)	None	✓				29.2.d.a	$1$	$0$	\(-1\)	\(0\)	\(3\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(2-2\beta _{1}+\beta _{2})q^{5}+\cdots\)
7569.2.a.q	$7569$	$2$	7569.a	1.a	$1$	$3$	$3$	$60.439$	3.3.733.1	None	✓				2523.2.a.i	$1$	$0$	\(-1\)	\(0\)	\(-3\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(3+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
7569.2.a.r	$7569$	$2$	7569.a	1.a	$1$	$3$	$3$	$60.439$	\(\Q(\zeta_{14})^+\)	None	✓				29.2.d.a	$1$	$0$	\(1\)	\(0\)	\(3\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(2-2\beta _{1}+\beta _{2})q^{5}+\cdots\)
7569.2.a.s	$7569$	$2$	7569.a	1.a	$1$	$3$	$3$	$60.439$	3.3.733.1	None	✓				2523.2.a.i	$1$	$1$	\(1\)	\(0\)	\(-3\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
7569.2.a.t	$7569$	$2$	7569.a	1.a	$1$	$3$	$3$	$60.439$	3.3.229.1	None	✓				87.2.a.b	$1$	$0$	\(2\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}+(2+\beta _{1})q^{4}+2\beta _{1}q^{5}+\cdots\)
7569.2.a.u	$7569$	$2$	7569.a	1.a	$1$	$4$	$4$	$60.439$	\(\Q(\zeta_{15})^+\)	\(\Q(\sqrt{-3}) \)	✓	✓			7569.2.a.u	$2$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+(-1+3\beta _{1}-\beta _{3})q^{7}+(4\beta _{2}+\cdots)q^{13}+\cdots\)
7569.2.a.v	$7569$	$2$	7569.a	1.a	$1$	$4$	$4$	$60.439$	\(\Q(\zeta_{15})^+\)	\(\Q(\sqrt{-3}) \)	✓	✓			7569.2.a.u	$2$	$0$	\(0\)	\(0\)	\(0\)	\(1\)		$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+(-1+3\beta _{1}-\beta _{3})q^{7}+(4\beta _{2}+\cdots)q^{13}+\cdots\)
7569.2.a.w	$7569$	$2$	7569.a	1.a	$1$	$4$	$4$	$60.439$	\(\Q(\sqrt{18 +2 \sqrt{5}})\)	None	✓	✓			7569.2.a.w	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}+\beta _{3}q^{5}+(-2+\cdots)q^{7}+\cdots\)
7569.2.a.x	$7569$	$2$	7569.a	1.a	$1$	$4$	$4$	$60.439$	\(\Q(\sqrt{18 +2 \sqrt{5}})\)	None	✓	✓			7569.2.a.w	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}-\beta _{3}q^{5}+(-2+\cdots)q^{7}+\cdots\)
7569.2.a.y	$7569$	$2$	7569.a	1.a	$1$	$6$	$6$	$60.439$	6.6.11973625.1	None	✓				841.2.a.g	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2-\beta _{3}+\beta _{4})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
7569.2.a.z	$7569$	$2$	7569.a	1.a	$1$	$6$	$6$	$60.439$	6.6.8902000.1	None	✓				2523.2.a.k	$1$	$0$	\(-1\)	\(0\)	\(-5\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2}-\beta _{3}+\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots\)
7569.2.a.ba	$7569$	$2$	7569.a	1.a	$1$	$6$	$6$	$60.439$	6.6.160016229.2	\(\Q(\sqrt{-87}) \)	✓				261.2.c.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$2^{3}$	$N(\mathrm{U}(1))$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
7569.2.a.bb	$7569$	$2$	7569.a	1.a	$1$	$6$	$6$	$60.439$	6.6.8902000.1	None	✓				2523.2.a.k	$1$	$1$	\(1\)	\(0\)	\(-5\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2}-\beta _{3}+\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots\)
7569.2.a.bc	$7569$	$2$	7569.a	1.a	$1$	$6$	$6$	$60.439$	6.6.11973625.1	None	✓				841.2.a.g	$1$	$0$	\(2\)	\(0\)	\(2\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2-\beta _{3}+\beta _{4})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
7569.2.a.bd	$7569$	$2$	7569.a	1.a	$1$	$8$	$8$	$60.439$	8.8.2841328125.1	None	✓				841.2.a.i	$1$	$1$	\(-4\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{3}-\beta _{6})q^{5}+\cdots\)
7569.2.a.be	$7569$	$2$	7569.a	1.a	$1$	$8$	$8$	$60.439$	8.8.5878828125.1	None	✓				2523.2.a.m	$1$	$0$	\(-1\)	\(0\)	\(9\)	\(-12\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
7569.2.a.bf	$7569$	$2$	7569.a	1.a	$1$	$8$	$8$	$60.439$	8.8.\(\cdots\).2	None	✓	✓			7569.2.a.bf	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-\beta _{6}+\cdots)q^{5}+\cdots\)
7569.2.a.bg	$7569$	$2$	7569.a	1.a	$1$	$8$	$8$	$60.439$	8.8.\(\cdots\).2	None	✓	✓			7569.2.a.bf	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{6}-\beta _{7})q^{5}+\cdots\)
7569.2.a.bh	$7569$	$2$	7569.a	1.a	$1$	$8$	$8$	$60.439$	8.8.5878828125.1	None	✓				2523.2.a.m	$1$	$1$	\(1\)	\(0\)	\(9\)	\(-12\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
7569.2.a.bi	$7569$	$2$	7569.a	1.a	$1$	$8$	$8$	$60.439$	8.8.2841328125.1	None	✓				841.2.a.i	$1$	$0$	\(4\)	\(0\)	\(1\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{3}-\beta _{6})q^{5}+\cdots\)
7569.2.a.bj	$7569$	$2$	7569.a	1.a	$1$	$9$	$9$	$60.439$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				87.2.g.a	$1$	$0$	\(-5\)	\(0\)	\(4\)	\(5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
7569.2.a.bk	$7569$	$2$	7569.a	1.a	$1$	$9$	$9$	$60.439$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				87.2.g.b	$1$	$0$	\(-1\)	\(0\)	\(0\)	\(5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\)
7569.2.a.bl	$7569$	$2$	7569.a	1.a	$1$	$9$	$9$	$60.439$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				87.2.g.b	$1$	$0$	\(1\)	\(0\)	\(0\)	\(5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\)
7569.2.a.bm	$7569$	$2$	7569.a	1.a	$1$	$9$	$9$	$60.439$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				87.2.g.a	$1$	$0$	\(5\)	\(0\)	\(4\)	\(5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
7569.2.a.bn	$7569$	$2$	7569.a	1.a	$1$	$12$	$12$	$60.439$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				87.2.i.a	$1$	$1$	\(-6\)	\(0\)	\(-2\)	\(-10\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots\)
7569.2.a.bo	$7569$	$2$	7569.a	1.a	$1$	$12$	$12$	$60.439$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				2523.2.a.t	$1$	$1$	\(-1\)	\(0\)	\(-7\)	\(9\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{3}-\beta _{6}+\beta _{9})q^{4}+(-1+\cdots)q^{5}+\cdots\)
7569.2.a.bp	$7569$	$2$	7569.a	1.a	$1$	$12$	$12$	$60.439$	12.12.\(\cdots\).1	None	✓				29.2.e.a	$2$	$1$	\(0\)	\(0\)	\(-8\)	\(10\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{11}q^{2}+(1-\beta _{1}-\beta _{2}+\beta _{7}-\beta _{10}+\cdots)q^{4}+\cdots\)
7569.2.a.bq	$7569$	$2$	7569.a	1.a	$1$	$12$	$12$	$60.439$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				261.2.k.d	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-14\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{11}q^{5}+(-1+\cdots)q^{7}+\cdots\)
7569.2.a.br	$7569$	$2$	7569.a	1.a	$1$	$12$	$12$	$60.439$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				261.2.k.d	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-14\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{11}q^{5}+(-1+\cdots)q^{7}+\cdots\)
7569.2.a.bs	$7569$	$2$	7569.a	1.a	$1$	$12$	$12$	$60.439$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		2523.2.a.t	$1$	$0$	\(1\)	\(0\)	\(-7\)	\(9\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{3}-\beta _{6}+\beta _{9})q^{4}+(-1+\cdots)q^{5}+\cdots\)
7569.2.a.bt	$7569$	$2$	7569.a	1.a	$1$	$12$	$12$	$60.439$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				87.2.i.a	$1$	$1$	\(6\)	\(0\)	\(-2\)	\(-10\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots\)
7569.2.a.bu	$7569$	$2$	7569.a	1.a	$1$	$16$	$16$	$60.439$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	✓	✓		7569.2.a.bu	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{1}-\beta _{10}+\cdots)q^{5}+\cdots\)
7569.2.a.bv	$7569$	$2$	7569.a	1.a	$1$	$16$	$16$	$60.439$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	✓			7569.2.a.bu	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(\beta _{1}+\beta _{10})q^{5}+\cdots\)
7569.2.a.bw	$7569$	$2$	7569.a	1.a	$1$	$36$	$36$	$60.439$		None	✓		✓		261.2.o.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(28\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7569))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7569)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(87))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(261))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(841))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2523))\)\(^{\oplus 2}\)