Space of modular forms of level 9405, weight 2, and trivial character

• Label: 9405.2.a
• Level: $9405$
• Weight: $2$
• Character orbit: 9405.a
• Rep. character: $\chi_{9405}(1,\cdot)$
• Character field: $\Q$
• Dimension: $300$
• Newform subspaces: $48$
• Sturm bound: $2880$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 9405 = 3^{2} \cdot 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9405.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 48 \)
Sturm bound:			\(2880\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(7\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9405))\).

	Total	New	Old
Modular forms	1456	300	1156
Cusp forms	1425	300	1125
Eisenstein series	31	0	31

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

\(3\)	\(5\)	\(11\)	\(19\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(15\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(19\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(15\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(11\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(15\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(11\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(15\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(19\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(23\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(21\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(23\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(25\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(22\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(24\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(22\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(20\)
Plus space				\(+\)	\(138\)
Minus space				\(-\)	\(162\)

Trace form

\( 300 q + 300 q^{4} - 4 q^{5} - 24 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9405))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	19
9405.2.a.a	$9405$	$2$	9405.a	1.a	$1$	$1$	$1$	$75.099$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+q^{5}-2q^{7}-2q^{10}+\cdots\)
9405.2.a.b	$9405$	$2$	9405.a	1.a	$1$	$1$	$1$	$75.099$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+q^{5}-2q^{10}-q^{11}+\cdots\)
9405.2.a.c	$9405$	$2$	9405.a	1.a	$1$	$1$	$1$	$75.099$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(1\)	\(4\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+q^{5}+4q^{7}-2q^{10}+\cdots\)
9405.2.a.d	$9405$	$2$	9405.a	1.a	$1$	$1$	$1$	$75.099$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}+3q^{8}+q^{10}+q^{11}+\cdots\)
9405.2.a.e	$9405$	$2$	9405.a	1.a	$1$	$1$	$1$	$75.099$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-1\)	\(4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots\)
9405.2.a.f	$9405$	$2$	9405.a	1.a	$1$	$1$	$1$	$75.099$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-1\)	\(4\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots\)
9405.2.a.g	$9405$	$2$	9405.a	1.a	$1$	$1$	$1$	$75.099$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}-q^{11}+\cdots\)
9405.2.a.h	$9405$	$2$	9405.a	1.a	$1$	$1$	$1$	$75.099$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}+q^{11}+\cdots\)
9405.2.a.i	$9405$	$2$	9405.a	1.a	$1$	$1$	$1$	$75.099$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(-4\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-4q^{7}-3q^{8}+q^{10}+\cdots\)
9405.2.a.j	$9405$	$2$	9405.a	1.a	$1$	$1$	$1$	$75.099$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots\)
9405.2.a.k	$9405$	$2$	9405.a	1.a	$1$	$1$	$1$	$75.099$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(4\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}+4q^{7}-3q^{8}+q^{10}+\cdots\)
9405.2.a.l	$9405$	$2$	9405.a	1.a	$1$	$1$	$1$	$75.099$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{5}-2q^{7}-2q^{10}+\cdots\)
9405.2.a.m	$9405$	$2$	9405.a	1.a	$1$	$1$	$1$	$75.099$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{5}-2q^{10}+q^{11}+\cdots\)
9405.2.a.n	$9405$	$2$	9405.a	1.a	$1$	$1$	$1$	$75.099$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(-1\)	\(4\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{5}+4q^{7}-2q^{10}+\cdots\)
9405.2.a.o	$9405$	$2$	9405.a	1.a	$1$	$2$	$2$	$75.099$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-q^{5}+2\beta q^{7}+\cdots\)
9405.2.a.p	$9405$	$2$	9405.a	1.a	$1$	$3$	$3$	$75.099$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(-3\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
9405.2.a.q	$9405$	$2$	9405.a	1.a	$1$	$3$	$3$	$75.099$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-3\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
9405.2.a.r	$9405$	$2$	9405.a	1.a	$1$	$3$	$3$	$75.099$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(-3\)	\(-5\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
9405.2.a.s	$9405$	$2$	9405.a	1.a	$1$	$3$	$3$	$75.099$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(3\)	\(-3\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
9405.2.a.t	$9405$	$2$	9405.a	1.a	$1$	$4$	$4$	$75.099$	4.4.132889.1	None	✓	$1$	$1$	\(1\)	\(0\)	\(-4\)	\(-5\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}-q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
9405.2.a.u	$9405$	$2$	9405.a	1.a	$1$	$5$	$5$	$75.099$	5.5.36497.1	None	✓	$1$	$0$	\(1\)	\(0\)	\(5\)	\(3\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{2}+\beta _{3}q^{4}+q^{5}+(1+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
9405.2.a.v	$9405$	$2$	9405.a	1.a	$1$	$5$	$5$	$75.099$	\(\Q(\zeta_{22})^+\)	None	✓	$1$	$0$	\(3\)	\(0\)	\(-5\)	\(-11\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{3}-\beta _{4})q^{2}+(1+\beta _{1}+\beta _{4})q^{4}+\cdots\)
9405.2.a.w	$9405$	$2$	9405.a	1.a	$1$	$6$	$6$	$75.099$	6.6.131947641.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-6\)	\(5\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2}-\beta _{3})q^{4}-q^{5}+(1+\cdots)q^{7}+\cdots\)
9405.2.a.x	$9405$	$2$	9405.a	1.a	$1$	$6$	$6$	$75.099$	6.6.905177.1	None	✓	$1$	$0$	\(1\)	\(0\)	\(-6\)	\(3\)		$-$	$+$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}+(1+\beta _{1})q^{4}-q^{5}-\beta _{5}q^{7}+\cdots\)
9405.2.a.y	$9405$	$2$	9405.a	1.a	$1$	$6$	$6$	$75.099$	6.6.20413244.1	None	✓	$1$	$1$	\(2\)	\(0\)	\(6\)	\(-7\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{2}+\beta _{3})q^{4}+q^{5}+(-1+\cdots)q^{7}+\cdots\)
9405.2.a.z	$9405$	$2$	9405.a	1.a	$1$	$6$	$6$	$75.099$	6.6.7281497.1	None	✓	$1$	$0$	\(2\)	\(0\)	\(6\)	\(5\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{4}q^{2}+(\beta _{4}+\beta _{5})q^{4}+q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
9405.2.a.ba	$9405$	$2$	9405.a	1.a	$1$	$6$	$6$	$75.099$	6.6.31252925.1	None	✓	$1$	$0$	\(2\)	\(0\)	\(6\)	\(5\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)
9405.2.a.bb	$9405$	$2$	9405.a	1.a	$1$	$7$	$7$	$75.099$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-3\)	\(0\)	\(7\)	\(-3\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-1-\beta _{4}+\cdots)q^{7}+\cdots\)
9405.2.a.bc	$9405$	$2$	9405.a	1.a	$1$	$7$	$7$	$75.099$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-7\)	\(4\)		$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+\beta _{6}q^{4}-q^{5}+(-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
9405.2.a.bd	$9405$	$2$	9405.a	1.a	$1$	$7$	$7$	$75.099$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(7\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
9405.2.a.be	$9405$	$2$	9405.a	1.a	$1$	$7$	$7$	$75.099$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(0\)	\(7\)	\(3\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+(\beta _{4}+\cdots)q^{7}+\cdots\)
9405.2.a.bf	$9405$	$2$	9405.a	1.a	$1$	$8$	$8$	$75.099$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(6\)	\(0\)	\(-8\)	\(-11\)		$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
9405.2.a.bg	$9405$	$2$	9405.a	1.a	$1$	$9$	$9$	$75.099$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(-5\)	\(0\)	\(-9\)	\(5\)		$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
9405.2.a.bh	$9405$	$2$	9405.a	1.a	$1$	$9$	$9$	$75.099$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(-3\)	\(0\)	\(-9\)	\(13\)		$-$	$+$	$+$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(1+\beta _{4}+\cdots)q^{7}+\cdots\)
9405.2.a.bi	$9405$	$2$	9405.a	1.a	$1$	$9$	$9$	$75.099$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(-3\)	\(0\)	\(9\)	\(-9\)		$-$	$-$	$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{8})q^{4}+q^{5}+(-1+\cdots)q^{7}+\cdots\)
9405.2.a.bj	$9405$	$2$	9405.a	1.a	$1$	$9$	$9$	$75.099$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(-3\)	\(0\)	\(9\)	\(3\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\beta _{7}q^{7}+\cdots\)
9405.2.a.bk	$9405$	$2$	9405.a	1.a	$1$	$9$	$9$	$75.099$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-9\)	\(-3\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{6}q^{7}+\cdots\)
9405.2.a.bl	$9405$	$2$	9405.a	1.a	$1$	$9$	$9$	$75.099$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(9\)	\(7\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(1-\beta _{6}+\cdots)q^{7}+\cdots\)
9405.2.a.bm	$9405$	$2$	9405.a	1.a	$1$	$10$	$10$	$75.099$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(-4\)	\(0\)	\(10\)	\(5\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+\beta _{7}q^{7}+\cdots\)
9405.2.a.bn	$9405$	$2$	9405.a	1.a	$1$	$10$	$10$	$75.099$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-10\)	\(-8\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(-1+\beta _{8}+\cdots)q^{7}+\cdots\)
9405.2.a.bo	$9405$	$2$	9405.a	1.a	$1$	$10$	$10$	$75.099$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(10\)	\(-8\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(-1+\beta _{8}+\cdots)q^{7}+\cdots\)
9405.2.a.bp	$9405$	$2$	9405.a	1.a	$1$	$12$	$12$	$75.099$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-12\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+\beta _{4}q^{7}+\cdots\)
9405.2.a.bq	$9405$	$2$	9405.a	1.a	$1$	$14$	$14$	$75.099$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(14\)	\(-12\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-1-\beta _{6}+\cdots)q^{7}+\cdots\)
9405.2.a.br	$9405$	$2$	9405.a	1.a	$1$	$14$	$14$	$75.099$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-14\)	\(-12\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(-1-\beta _{6}+\cdots)q^{7}+\cdots\)
9405.2.a.bs	$9405$	$2$	9405.a	1.a	$1$	$15$	$15$	$75.099$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-15\)	\(4\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{9}q^{7}+\cdots\)
9405.2.a.bt	$9405$	$2$	9405.a	1.a	$1$	$15$	$15$	$75.099$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(15\)	\(4\)		$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+\beta _{9}q^{7}+\cdots\)
9405.2.a.bu	$9405$	$2$	9405.a	1.a	$1$	$19$	$19$	$75.099$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	$1$	$0$	\(-3\)	\(0\)	\(-19\)	\(12\)		$+$	$+$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(1-\beta _{8}+\cdots)q^{7}+\cdots\)
9405.2.a.bv	$9405$	$2$	9405.a	1.a	$1$	$19$	$19$	$75.099$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(0\)	\(19\)	\(12\)		$+$	$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(1-\beta _{8}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9405))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9405)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(209))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(285))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(495))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(627))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(855))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1045))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1881))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3135))\)\(^{\oplus 2}\)