Space of modular forms of level 2205, weight 2, and trivial character

• Label: 2205.2.a
• Level: $2205$
• Weight: $2$
• Character orbit: 2205.a
• Rep. character: $\chi_{2205}(1,\cdot)$
• Character field: $\Q$
• Dimension: $69$
• Newform subspaces: $35$
• Sturm bound: $672$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2205.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 35 \)
Sturm bound:			\(672\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(2\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2205))\).

	Total	New	Old
Modular forms	368	69	299
Cusp forms	305	69	236
Eisenstein series	63	0	63

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

\(3\)	\(5\)	\(7\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(7\)
\(+\)	\(+\)	\(-\)	$-$	\(7\)
\(+\)	\(-\)	\(+\)	$-$	\(7\)
\(+\)	\(-\)	\(-\)	$+$	\(7\)
\(-\)	\(+\)	\(+\)	$-$	\(11\)
\(-\)	\(+\)	\(-\)	$+$	\(9\)
\(-\)	\(-\)	\(+\)	$+$	\(9\)
\(-\)	\(-\)	\(-\)	$-$	\(12\)
Plus space			\(+\)	\(32\)
Minus space			\(-\)	\(37\)

Trace form

\( 69 q - 3 q^{2} + 67 q^{4} + q^{5} - 15 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2205))\) 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	7
2205.2.a.a	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}+3q^{8}+q^{10}+2q^{11}+\cdots\)
2205.2.a.b	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{5}+3q^{8}-q^{10}+6q^{13}+\cdots\)
2205.2.a.c	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{5}+3q^{8}-q^{10}+2q^{11}+\cdots\)
2205.2.a.d	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-q^{5}+q^{13}+4q^{16}+6q^{17}+\cdots\)
2205.2.a.e	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-q^{5}+3q^{11}-5q^{13}+4q^{16}+\cdots\)
2205.2.a.f	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{5}-q^{13}+4q^{16}-6q^{17}+\cdots\)
2205.2.a.g	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}-3q^{8}-q^{10}-2q^{11}+\cdots\)
2205.2.a.h	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-3q^{8}+q^{10}-2q^{11}+\cdots\)
2205.2.a.i	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-3q^{8}+q^{10}+4q^{11}+\cdots\)
2205.2.a.j	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{5}-2q^{10}-q^{11}+\cdots\)
2205.2.a.k	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{5}-2q^{10}+6q^{11}+\cdots\)
2205.2.a.l	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+q^{5}+2q^{10}-q^{11}+\cdots\)
2205.2.a.m	$2205$	$2$	2205.a	1.a	$1$	$1$	$1$	$17.607$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+q^{5}+2q^{10}+6q^{11}+\cdots\)
2205.2.a.n	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-q^{5}+(-3+\cdots)q^{8}+\cdots\)
2205.2.a.o	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-q^{5}+(-3+\cdots)q^{8}+\cdots\)
2205.2.a.p	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(-3+\cdots)q^{8}+\cdots\)
2205.2.a.q	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(-3+\cdots)q^{8}+\cdots\)
2205.2.a.r	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(-3+\cdots)q^{8}+\cdots\)
2205.2.a.s	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{5}-2\beta q^{8}-\beta q^{10}+(-2+\cdots)q^{11}+\cdots\)
2205.2.a.t	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{5}-2\beta q^{8}-\beta q^{10}+(3-2\beta )q^{11}+\cdots\)
2205.2.a.u	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{5}-2\beta q^{8}+\beta q^{10}+(-2+\cdots)q^{11}+\cdots\)
2205.2.a.v	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{5}-2\beta q^{8}+\beta q^{10}+(3-2\beta )q^{11}+\cdots\)
2205.2.a.w	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+3q^{4}-q^{5}-\beta q^{8}+\beta q^{10}+\cdots\)
2205.2.a.x	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(1\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(2+\beta )q^{4}+q^{5}+(4+\beta )q^{8}+\cdots\)
2205.2.a.y	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-q^{5}+(3+\beta )q^{8}+\cdots\)
2205.2.a.z	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(2+2\beta )q^{4}-q^{5}+(6+2\beta )q^{8}+\cdots\)
2205.2.a.ba	$2205$	$2$	2205.a	1.a	$1$	$2$	$2$	$17.607$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(2+2\beta )q^{4}+q^{5}+(6+2\beta )q^{8}+\cdots\)
2205.2.a.bb	$2205$	$2$	2205.a	1.a	$1$	$3$	$3$	$17.607$	3.3.404.1	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-3\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2205.2.a.bc	$2205$	$2$	2205.a	1.a	$1$	$3$	$3$	$17.607$	3.3.404.1	None	✓	$1$	$1$	\(-2\)	\(0\)	\(3\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2205.2.a.bd	$2205$	$2$	2205.a	1.a	$1$	$3$	$3$	$17.607$	3.3.404.1	None	✓	$1$	$0$	\(2\)	\(0\)	\(-3\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
2205.2.a.be	$2205$	$2$	2205.a	1.a	$1$	$3$	$3$	$17.607$	3.3.404.1	None	✓	$1$	$0$	\(2\)	\(0\)	\(3\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
2205.2.a.bf	$2205$	$2$	2205.a	1.a	$1$	$4$	$4$	$17.607$	4.4.4352.1	None	✓	$1$	$0$	\(-4\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1}+\beta _{3})q^{2}+(2+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
2205.2.a.bg	$2205$	$2$	2205.a	1.a	$1$	$4$	$4$	$17.607$	4.4.4352.1	None	✓	$1$	$1$	\(-4\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1}+\beta _{3})q^{2}+(2+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
2205.2.a.bh	$2205$	$2$	2205.a	1.a	$1$	$4$	$4$	$17.607$	\(\Q(\zeta_{24})^+\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+\beta _{3}q^{8}-\beta _{1}q^{10}+\cdots\)
2205.2.a.bi	$2205$	$2$	2205.a	1.a	$1$	$4$	$4$	$17.607$	\(\Q(\zeta_{24})^+\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+\beta _{3}q^{8}+\beta _{1}q^{10}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2205))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2205)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(441))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(735))\)\(^{\oplus 2}\)