Space of modular forms of level 2904, weight 2, and trivial character

• Label: 2904.2.a
• Level: $2904$
• Weight: $2$
• Character orbit: 2904.a
• Rep. character: $\chi_{2904}(1,\cdot)$
• Character field: $\Q$
• Dimension: $55$
• Newform subspaces: $31$
• Sturm bound: $1056$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 2904 = 2^{3} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2904.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 31 \)
Sturm bound:			\(1056\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2904))\).

	Total	New	Old
Modular forms	576	55	521
Cusp forms	481	55	426
Eisenstein series	95	0	95

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

\(2\)	\(3\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(8\)
\(+\)	\(+\)	\(-\)	$-$	\(6\)
\(+\)	\(-\)	\(+\)	$-$	\(7\)
\(+\)	\(-\)	\(-\)	$+$	\(6\)
\(-\)	\(+\)	\(+\)	$-$	\(10\)
\(-\)	\(+\)	\(-\)	$+$	\(4\)
\(-\)	\(-\)	\(+\)	$+$	\(5\)
\(-\)	\(-\)	\(-\)	$-$	\(9\)
Plus space			\(+\)	\(23\)
Minus space			\(-\)	\(32\)

Trace form

\( 55 q - q^{3} - 2 q^{5} - 4 q^{7} + 55 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2904))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	11
2904.2.a.a	$2904$	$2$	2904.a	1.a	$1$	$1$	$1$	$23.189$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}-4q^{7}+q^{9}+6q^{13}+\cdots\)
2904.2.a.b	$2904$	$2$	2904.a	1.a	$1$	$1$	$1$	$23.189$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-4\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-4q^{5}+4q^{7}+q^{9}-6q^{13}+\cdots\)
2904.2.a.c	$2904$	$2$	2904.a	1.a	$1$	$1$	$1$	$23.189$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}+2q^{13}+2q^{15}+\cdots\)
2904.2.a.d	$2904$	$2$	2904.a	1.a	$1$	$1$	$1$	$23.189$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}-q^{13}+q^{15}+3q^{17}+\cdots\)
2904.2.a.e	$2904$	$2$	2904.a	1.a	$1$	$1$	$1$	$23.189$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+q^{13}+q^{15}-3q^{17}+\cdots\)
2904.2.a.f	$2904$	$2$	2904.a	1.a	$1$	$1$	$1$	$23.189$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-2q^{7}+q^{9}-2q^{15}+\cdots\)
2904.2.a.g	$2904$	$2$	2904.a	1.a	$1$	$1$	$1$	$23.189$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots\)
2904.2.a.h	$2904$	$2$	2904.a	1.a	$1$	$1$	$1$	$23.189$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+2q^{7}+q^{9}-2q^{15}+\cdots\)
2904.2.a.i	$2904$	$2$	2904.a	1.a	$1$	$1$	$1$	$23.189$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-4q^{7}+q^{9}-6q^{13}+\cdots\)
2904.2.a.j	$2904$	$2$	2904.a	1.a	$1$	$1$	$1$	$23.189$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-2q^{7}+q^{9}+4q^{13}+\cdots\)
2904.2.a.k	$2904$	$2$	2904.a	1.a	$1$	$1$	$1$	$23.189$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+2q^{7}+q^{9}-4q^{13}+\cdots\)
2904.2.a.l	$2904$	$2$	2904.a	1.a	$1$	$1$	$1$	$23.189$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}+q^{9}+2q^{17}-8q^{19}+\cdots\)
2904.2.a.m	$2904$	$2$	2904.a	1.a	$1$	$1$	$1$	$23.189$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{7}+q^{9}+6q^{13}+4q^{17}+\cdots\)
2904.2.a.n	$2904$	$2$	2904.a	1.a	$1$	$1$	$1$	$23.189$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{7}+q^{9}-6q^{13}-4q^{17}+\cdots\)
2904.2.a.o	$2904$	$2$	2904.a	1.a	$1$	$1$	$1$	$23.189$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(4\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}+2q^{7}+q^{9}+4q^{15}+\cdots\)
2904.2.a.p	$2904$	$2$	2904.a	1.a	$1$	$2$	$2$	$23.189$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta q^{5}+(1-2\beta )q^{7}+q^{9}+(-3+\cdots)q^{13}+\cdots\)
2904.2.a.q	$2904$	$2$	2904.a	1.a	$1$	$2$	$2$	$23.189$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta q^{5}+(-1+2\beta )q^{7}+q^{9}+\cdots\)
2904.2.a.r	$2904$	$2$	2904.a	1.a	$1$	$2$	$2$	$23.189$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-5\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2-\beta )q^{5}+(-3+2\beta )q^{7}+\cdots\)
2904.2.a.s	$2904$	$2$	2904.a	1.a	$1$	$2$	$2$	$23.189$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-5\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-2-\beta )q^{5}+(3-2\beta )q^{7}+q^{9}+\cdots\)
2904.2.a.t	$2904$	$2$	2904.a	1.a	$1$	$2$	$2$	$23.189$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta q^{5}+(-1+\beta )q^{7}+q^{9}+(-2+\cdots)q^{13}+\cdots\)
2904.2.a.u	$2904$	$2$	2904.a	1.a	$1$	$2$	$2$	$23.189$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta q^{5}+(1-\beta )q^{7}+q^{9}+(2-\beta )q^{13}+\cdots\)
2904.2.a.v	$2904$	$2$	2904.a	1.a	$1$	$2$	$2$	$23.189$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(1\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+3\beta )q^{5}-3\beta q^{7}+q^{9}+\cdots\)
2904.2.a.w	$2904$	$2$	2904.a	1.a	$1$	$2$	$2$	$23.189$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(1\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1+3\beta )q^{5}+3\beta q^{7}+q^{9}+\cdots\)
2904.2.a.x	$2904$	$2$	2904.a	1.a	$1$	$2$	$2$	$23.189$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(2\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{7}+q^{9}+(-2-\beta )q^{13}+\cdots\)
2904.2.a.y	$2904$	$2$	2904.a	1.a	$1$	$2$	$2$	$23.189$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+2q^{7}+q^{9}+(2+\beta )q^{13}+\cdots\)
2904.2.a.z	$2904$	$2$	2904.a	1.a	$1$	$2$	$2$	$23.189$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(3\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}+(-3+2\beta )q^{7}+q^{9}+\cdots\)
2904.2.a.ba	$2904$	$2$	2904.a	1.a	$1$	$2$	$2$	$23.189$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(3\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta )q^{5}+(3-2\beta )q^{7}+q^{9}+\cdots\)
2904.2.a.bb	$2904$	$2$	2904.a	1.a	$1$	$4$	$4$	$23.189$	4.4.13625.1	None	✓	$1$	$0$	\(0\)	\(-4\)	\(2\)	\(-5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}+(-2+\beta _{2}-2\beta _{3})q^{7}+\cdots\)
2904.2.a.bc	$2904$	$2$	2904.a	1.a	$1$	$4$	$4$	$23.189$	4.4.46224.1	None	✓	$1$	$1$	\(0\)	\(-4\)	\(2\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}+(-1-\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots\)
2904.2.a.bd	$2904$	$2$	2904.a	1.a	$1$	$4$	$4$	$23.189$	4.4.46224.1	None	✓	$1$	$0$	\(0\)	\(-4\)	\(2\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}+(1+\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots\)
2904.2.a.be	$2904$	$2$	2904.a	1.a	$1$	$4$	$4$	$23.189$	4.4.13625.1	None	✓	$1$	$0$	\(0\)	\(-4\)	\(2\)	\(5\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}+(2-\beta _{2}+2\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2904))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2904)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(484))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(726))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(968))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1452))\)\(^{\oplus 2}\)