Space of modular forms of level 1815, weight 4, and trivial character

• Label: 1815.4.a
• Level: $1815$
• Weight: $4$
• Character orbit: 1815.a
• Rep. character: $\chi_{1815}(1,\cdot)$
• Character field: $\Q$
• Dimension: $218$
• Newform subspaces: $41$
• Sturm bound: $1056$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1815.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 41 \)
Sturm bound:			\(1056\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1815))\).

	Total	New	Old
Modular forms	816	218	598
Cusp forms	768	218	550
Eisenstein series	48	0	48

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

\(3\)	\(5\)	\(11\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(108\)	\(28\)	\(80\)		\(102\)	\(28\)	\(74\)		\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(-\)	\(-\)		\(96\)	\(27\)	\(69\)		\(90\)	\(27\)	\(63\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(96\)	\(22\)	\(74\)		\(90\)	\(22\)	\(68\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(108\)	\(32\)	\(76\)		\(102\)	\(32\)	\(70\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(102\)	\(26\)	\(76\)		\(96\)	\(26\)	\(70\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(102\)	\(28\)	\(74\)		\(96\)	\(28\)	\(68\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(102\)	\(32\)	\(70\)		\(96\)	\(32\)	\(64\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(102\)	\(23\)	\(79\)		\(96\)	\(23\)	\(73\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(420\)	\(120\)	\(300\)		\(396\)	\(120\)	\(276\)		\(24\)	\(0\)	\(24\)
Minus space			\(-\)		\(396\)	\(98\)	\(298\)		\(372\)	\(98\)	\(274\)		\(24\)	\(0\)	\(24\)

Trace form

218 * q - 4 * q^2 + 898 * q^4 - 6 * q^6 - 60 * q^7 + 36 * q^8 + 1962 * q^9 - 50 * q^10 - 24 * q^12 - 40 * q^13 - 36 * q^14 + 30 * q^15 + 3514 * q^16 + 88 * q^17 - 36 * q^18 - 8 * q^19 + 40 * q^20 - 132 * q^21 + 272 * q^23 - 342 * q^24 + 5450 * q^25 + 756 * q^26 - 164 * q^28 - 88 * q^29 - 60 * q^30 - 64 * q^31 + 164 * q^32 - 364 * q^34 + 300 * q^35 + 8082 * q^36 - 568 * q^37 + 496 * q^38 - 180 * q^39 - 450 * q^40 + 204 * q^41 + 588 * q^42 + 880 * q^43 - 736 * q^46 - 648 * q^47 - 912 * q^48 + 11298 * q^49 - 100 * q^50 - 300 * q^51 + 112 * q^52 - 256 * q^53 - 54 * q^54 + 540 * q^56 - 144 * q^57 + 3116 * q^58 - 156 * q^59 - 90 * q^60 - 1116 * q^61 + 4816 * q^62 - 540 * q^63 + 15938 * q^64 + 580 * q^65 + 392 * q^67 + 984 * q^68 + 1152 * q^69 + 980 * q^70 + 2440 * q^71 + 324 * q^72 - 2548 * q^73 + 4868 * q^74 - 560 * q^76 + 168 * q^78 + 672 * q^79 + 1200 * q^80 + 17658 * q^81 - 4416 * q^82 + 808 * q^83 - 3228 * q^84 - 1020 * q^85 - 32 * q^86 - 60 * q^87 - 1804 * q^89 - 450 * q^90 + 5640 * q^91 + 3848 * q^92 + 4056 * q^93 + 6776 * q^94 + 520 * q^95 - 2862 * q^96 + 3076 * q^97 - 2668 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1815))\) 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	5	11
1815.4.a.a	$1815$	$4$	1815.a	1.a	$1$	$1$	$1$	$107.088$	\(\Q\)	None	✓				15.4.a.b	$1$	$1$	\(-3\)	\(-3\)	\(-5\)	\(-20\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{2}-3q^{3}+q^{4}-5q^{5}+9q^{6}+\cdots\)
1815.4.a.b	$1815$	$4$	1815.a	1.a	$1$	$1$	$1$	$107.088$	\(\Q\)	None	✓	✓			1815.4.a.b	$1$	$1$	\(-1\)	\(-3\)	\(-5\)	\(33\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-3q^{3}-7q^{4}-5q^{5}+3q^{6}+\cdots\)
1815.4.a.c	$1815$	$4$	1815.a	1.a	$1$	$1$	$1$	$107.088$	\(\Q\)	None	✓				165.4.a.b	$1$	$2$	\(-1\)	\(3\)	\(-5\)	\(-36\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}-7q^{4}-5q^{5}-3q^{6}+\cdots\)
1815.4.a.d	$1815$	$4$	1815.a	1.a	$1$	$1$	$1$	$107.088$	\(\Q\)	None	✓	✓			1815.4.a.d	$1$	$1$	\(-1\)	\(3\)	\(5\)	\(-9\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}-7q^{4}+5q^{5}-3q^{6}+\cdots\)
1815.4.a.e	$1815$	$4$	1815.a	1.a	$1$	$1$	$1$	$107.088$	\(\Q\)	None	✓				15.4.a.a	$1$	$1$	\(-1\)	\(3\)	\(5\)	\(24\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}-7q^{4}+5q^{5}-3q^{6}+\cdots\)
1815.4.a.f	$1815$	$4$	1815.a	1.a	$1$	$1$	$1$	$107.088$	\(\Q\)	None	✓				165.4.a.a	$1$	$1$	\(0\)	\(-3\)	\(-5\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-8q^{4}-5q^{5}-2q^{7}+9q^{9}+\cdots\)
1815.4.a.g	$1815$	$4$	1815.a	1.a	$1$	$1$	$1$	$107.088$	\(\Q\)	None	✓	✓			1815.4.a.b	$1$	$1$	\(1\)	\(-3\)	\(-5\)	\(-33\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-3q^{3}-7q^{4}-5q^{5}-3q^{6}+\cdots\)
1815.4.a.h	$1815$	$4$	1815.a	1.a	$1$	$1$	$1$	$107.088$	\(\Q\)	None	✓	✓			1815.4.a.d	$1$	$1$	\(1\)	\(3\)	\(5\)	\(9\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+3q^{3}-7q^{4}+5q^{5}+3q^{6}+\cdots\)
1815.4.a.i	$1815$	$4$	1815.a	1.a	$1$	$2$	$2$	$107.088$	\(\Q(\sqrt{41}) \)	None	✓	✓			1815.4.a.i	$1$	$1$	\(-1\)	\(6\)	\(10\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+3q^{3}+(2+\beta )q^{4}+5q^{5}-3\beta q^{6}+\cdots\)
1815.4.a.j	$1815$	$4$	1815.a	1.a	$1$	$2$	$2$	$107.088$	\(\Q(\sqrt{5}) \)	None	✓	✓			1815.4.a.j	$2$	$1$	\(0\)	\(6\)	\(-10\)	\(0\)		$-$	$+$	$+$	$-$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	\(q+3q^{3}-8q^{4}-5q^{5}+\beta q^{7}+9q^{9}+\cdots\)
1815.4.a.k	$1815$	$4$	1815.a	1.a	$1$	$2$	$2$	$107.088$	\(\Q(\sqrt{3}) \)	None	✓	✓			1815.4.a.k	$2$	$1$	\(0\)	\(6\)	\(-10\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{2}+3q^{3}+4q^{4}-5q^{5}+6\beta q^{6}+\cdots\)
1815.4.a.l	$1815$	$4$	1815.a	1.a	$1$	$2$	$2$	$107.088$	\(\Q(\sqrt{3}) \)	None	✓	✓			1815.4.a.l	$2$	$0$	\(0\)	\(6\)	\(10\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{2}+3q^{3}+4q^{4}+5q^{5}+6\beta q^{6}+\cdots\)
1815.4.a.m	$1815$	$4$	1815.a	1.a	$1$	$2$	$2$	$107.088$	\(\Q(\sqrt{15}) \)	None	✓	✓			1815.4.a.m	$2$	$1$	\(0\)	\(6\)	\(-10\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+3q^{3}+7q^{4}-5q^{5}+3\beta q^{6}+\cdots\)
1815.4.a.n	$1815$	$4$	1815.a	1.a	$1$	$2$	$2$	$107.088$	\(\Q(\sqrt{17}) \)	None	✓				165.4.a.c	$1$	$0$	\(1\)	\(6\)	\(-10\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+3q^{3}+(-4+\beta )q^{4}-5q^{5}+\cdots\)
1815.4.a.o	$1815$	$4$	1815.a	1.a	$1$	$2$	$2$	$107.088$	\(\Q(\sqrt{41}) \)	None	✓	✓			1815.4.a.i	$1$	$1$	\(1\)	\(6\)	\(10\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+3q^{3}+(2+\beta )q^{4}+5q^{5}+3\beta q^{6}+\cdots\)
1815.4.a.p	$1815$	$4$	1815.a	1.a	$1$	$3$	$3$	$107.088$	3.3.788.1	None	✓				165.4.a.f	$1$	$0$	\(-1\)	\(-9\)	\(15\)	\(16\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}-3q^{3}+(-2-\beta _{1})q^{4}+5q^{5}+\cdots\)
1815.4.a.q	$1815$	$4$	1815.a	1.a	$1$	$3$	$3$	$107.088$	3.3.1957.1	None	✓				165.4.a.g	$1$	$0$	\(-1\)	\(-9\)	\(15\)	\(-6\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-3q^{3}+(6+\beta _{1}+2\beta _{2})q^{4}+\cdots\)
1815.4.a.r	$1815$	$4$	1815.a	1.a	$1$	$3$	$3$	$107.088$	3.3.47528.1	None	✓				165.4.a.e	$1$	$0$	\(2\)	\(9\)	\(-15\)	\(-10\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+3q^{3}+(10+\beta _{2})q^{4}+\cdots\)
1815.4.a.s	$1815$	$4$	1815.a	1.a	$1$	$3$	$3$	$107.088$	3.3.23612.1	None	✓				165.4.a.d	$1$	$1$	\(4\)	\(-9\)	\(-15\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}-3q^{3}+(7+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1815.4.a.t	$1815$	$4$	1815.a	1.a	$1$	$4$	$4$	$107.088$	4.4.1540841.1	None	✓				165.4.a.h	$1$	$1$	\(-4\)	\(12\)	\(20\)	\(-34\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+3q^{3}+(7-\beta _{1}+\beta _{3})q^{4}+\cdots\)
1815.4.a.u	$1815$	$4$	1815.a	1.a	$1$	$4$	$4$	$107.088$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	✓			1815.4.a.u	$1$	$1$	\(-1\)	\(-12\)	\(-20\)	\(-45\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-3q^{3}+(6+\beta _{2})q^{4}-5q^{5}+\cdots\)
1815.4.a.v	$1815$	$4$	1815.a	1.a	$1$	$4$	$4$	$107.088$	4.4.744012.1	None	✓	✓			1815.4.a.v	$2$	$1$	\(0\)	\(-12\)	\(20\)	\(0\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-3q^{3}+(3+\beta _{3})q^{4}+5q^{5}+\cdots\)
1815.4.a.w	$1815$	$4$	1815.a	1.a	$1$	$4$	$4$	$107.088$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	✓			1815.4.a.u	$1$	$1$	\(1\)	\(-12\)	\(-20\)	\(45\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-3q^{3}+(6+\beta _{2})q^{4}-5q^{5}+\cdots\)
1815.4.a.x	$1815$	$4$	1815.a	1.a	$1$	$5$	$5$	$107.088$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓			1815.4.a.x	$1$	$0$	\(-1\)	\(15\)	\(-25\)	\(14\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+3q^{3}+(4+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1815.4.a.y	$1815$	$4$	1815.a	1.a	$1$	$5$	$5$	$107.088$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓			1815.4.a.x	$1$	$0$	\(1\)	\(15\)	\(-25\)	\(-14\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+3q^{3}+(4+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1815.4.a.z	$1815$	$4$	1815.a	1.a	$1$	$6$	$6$	$107.088$	6.6.7598722752.1	None	✓	✓			1815.4.a.z	$2$	$1$	\(0\)	\(-18\)	\(30\)	\(0\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{3})q^{2}-3q^{3}+(2-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
1815.4.a.ba	$1815$	$4$	1815.a	1.a	$1$	$6$	$6$	$107.088$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓			1815.4.a.ba	$2$	$0$	\(0\)	\(-18\)	\(-30\)	\(0\)		$+$	$+$	$+$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-3q^{3}+(7+\beta _{2})q^{4}-5q^{5}+\cdots\)
1815.4.a.bb	$1815$	$4$	1815.a	1.a	$1$	$6$	$6$	$107.088$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓			1815.4.a.bb	$2$	$0$	\(0\)	\(18\)	\(30\)	\(0\)		$-$	$-$	$+$	$+$	$2^{4}\cdot 5$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+3q^{3}+(7+\beta _{2})q^{4}+5q^{5}+\cdots\)
1815.4.a.bc	$1815$	$4$	1815.a	1.a	$1$	$7$	$7$	$107.088$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			1815.4.a.bc	$1$	$0$	\(-1\)	\(-21\)	\(35\)	\(16\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-3q^{3}+(7+\beta _{2})q^{4}+5q^{5}+\cdots\)
1815.4.a.bd	$1815$	$4$	1815.a	1.a	$1$	$7$	$7$	$107.088$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓			1815.4.a.bc	$1$	$0$	\(1\)	\(-21\)	\(35\)	\(-16\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-3q^{3}+(7+\beta _{2})q^{4}+5q^{5}+\cdots\)
1815.4.a.be	$1815$	$4$	1815.a	1.a	$1$	$8$	$8$	$107.088$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓			1815.4.a.be	$2$	$1$	\(0\)	\(24\)	\(-40\)	\(0\)		$-$	$+$	$+$	$-$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+3q^{3}+(6+\beta _{4})q^{4}-5q^{5}+\cdots\)
1815.4.a.bf	$1815$	$4$	1815.a	1.a	$1$	$10$	$10$	$107.088$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓			1815.4.a.bf	$2$	$0$	\(0\)	\(-30\)	\(-50\)	\(0\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-3q^{3}+(1+\beta _{2})q^{4}-5q^{5}+\cdots\)
1815.4.a.bg	$1815$	$4$	1815.a	1.a	$1$	$12$	$12$	$107.088$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		165.4.m.d	$1$	$1$	\(-9\)	\(36\)	\(-60\)	\(-21\)		$-$	$+$	$+$	$-$	$5\cdot 11^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+3q^{3}+(5-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1815.4.a.bh	$1815$	$4$	1815.a	1.a	$1$	$12$	$12$	$107.088$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		165.4.m.a	$1$	$1$	\(-7\)	\(36\)	\(60\)	\(-77\)		$-$	$-$	$-$	$-$	$5\cdot 11^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+3q^{3}+(5-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1815.4.a.bi	$1815$	$4$	1815.a	1.a	$1$	$12$	$12$	$107.088$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		165.4.m.c	$1$	$1$	\(-1\)	\(-36\)	\(60\)	\(5\)		$+$	$-$	$+$	$-$	$11^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+5q^{5}+\cdots\)
1815.4.a.bj	$1815$	$4$	1815.a	1.a	$1$	$12$	$12$	$107.088$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		165.4.m.b	$1$	$0$	\(-1\)	\(-36\)	\(-60\)	\(51\)		$+$	$+$	$+$	$+$	$11^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-3q^{3}+(5+\beta _{2})q^{4}-5q^{5}+\cdots\)
1815.4.a.bk	$1815$	$4$	1815.a	1.a	$1$	$12$	$12$	$107.088$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			1815.4.a.bk	$2$	$0$	\(0\)	\(36\)	\(60\)	\(0\)		$-$	$-$	$+$	$+$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+3q^{3}+(5+\beta _{2})q^{4}+5q^{5}+\cdots\)
1815.4.a.bl	$1815$	$4$	1815.a	1.a	$1$	$12$	$12$	$107.088$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		165.4.m.c	$1$	$0$	\(1\)	\(-36\)	\(60\)	\(-5\)		$+$	$-$	$-$	$+$	$11^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+5q^{5}+\cdots\)
1815.4.a.bm	$1815$	$4$	1815.a	1.a	$1$	$12$	$12$	$107.088$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		165.4.m.b	$1$	$1$	\(1\)	\(-36\)	\(-60\)	\(-51\)		$+$	$+$	$-$	$-$	$11^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-3q^{3}+(5+\beta _{2})q^{4}-5q^{5}+\cdots\)
1815.4.a.bn	$1815$	$4$	1815.a	1.a	$1$	$12$	$12$	$107.088$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				165.4.m.a	$1$	$0$	\(7\)	\(36\)	\(60\)	\(77\)		$-$	$-$	$+$	$+$	$5\cdot 11^{2}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+3q^{3}+(5-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1815.4.a.bo	$1815$	$4$	1815.a	1.a	$1$	$12$	$12$	$107.088$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		165.4.m.d	$1$	$0$	\(9\)	\(36\)	\(-60\)	\(21\)		$-$	$+$	$-$	$+$	$5\cdot 11^{2}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+3q^{3}+(5-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1815))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1815)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(605))\)\(^{\oplus 2}\)