Space of modular forms of level 2898, weight 2, and trivial character

• Label: 2898.2.a
• Level: $2898$
• Weight: $2$
• Character orbit: 2898.a
• Rep. character: $\chi_{2898}(1,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $35$
• Sturm bound: $1152$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2898 = 2 \cdot 3^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2898.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 35 \)
Sturm bound:			\(1152\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2898))\).

	Total	New	Old
Modular forms	592	56	536
Cusp forms	561	56	505
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.

\(2\)	\(3\)	\(7\)	\(23\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(3\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(3\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(1\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(5\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(4\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(4\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(1\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(5\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(3\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(5\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(2\)
Plus space				\(+\)	\(22\)
Minus space				\(-\)	\(34\)

Trace form

\( 56 q + 56 q^{4} + 4 q^{5} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2898))\) 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	7	23
2898.2.a.a	$2898$	$2$	2898.a	1.a	$1$	$1$	$1$	$23.141$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-3\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-3q^{5}-q^{7}-q^{8}+3q^{10}+\cdots\)
2898.2.a.b	$2898$	$2$	2898.a	1.a	$1$	$1$	$1$	$23.141$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-3\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-3q^{5}+q^{7}-q^{8}+3q^{10}+\cdots\)
2898.2.a.c	$2898$	$2$	2898.a	1.a	$1$	$1$	$1$	$23.141$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
2898.2.a.d	$2898$	$2$	2898.a	1.a	$1$	$1$	$1$	$23.141$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\)
2898.2.a.e	$2898$	$2$	2898.a	1.a	$1$	$1$	$1$	$23.141$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\)
2898.2.a.f	$2898$	$2$	2898.a	1.a	$1$	$1$	$1$	$23.141$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots\)
2898.2.a.g	$2898$	$2$	2898.a	1.a	$1$	$1$	$1$	$23.141$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots\)
2898.2.a.h	$2898$	$2$	2898.a	1.a	$1$	$1$	$1$	$23.141$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(1\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots\)
2898.2.a.i	$2898$	$2$	2898.a	1.a	$1$	$1$	$1$	$23.141$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots\)
2898.2.a.j	$2898$	$2$	2898.a	1.a	$1$	$1$	$1$	$23.141$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(3\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}+q^{7}-q^{8}-3q^{10}+\cdots\)
2898.2.a.k	$2898$	$2$	2898.a	1.a	$1$	$1$	$1$	$23.141$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-3\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}+q^{7}+q^{8}-3q^{10}+\cdots\)
2898.2.a.l	$2898$	$2$	2898.a	1.a	$1$	$1$	$1$	$23.141$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}+q^{7}+q^{8}-2q^{10}+\cdots\)
2898.2.a.m	$2898$	$2$	2898.a	1.a	$1$	$1$	$1$	$23.141$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
2898.2.a.n	$2898$	$2$	2898.a	1.a	$1$	$1$	$1$	$23.141$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{7}+q^{8}+2q^{11}-6q^{13}+\cdots\)
2898.2.a.o	$2898$	$2$	2898.a	1.a	$1$	$1$	$1$	$23.141$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{7}+q^{8}-6q^{11}+2q^{13}+\cdots\)
2898.2.a.p	$2898$	$2$	2898.a	1.a	$1$	$1$	$1$	$23.141$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{7}+q^{8}-4q^{11}+q^{14}+\cdots\)
2898.2.a.q	$2898$	$2$	2898.a	1.a	$1$	$1$	$1$	$23.141$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(1\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
2898.2.a.r	$2898$	$2$	2898.a	1.a	$1$	$1$	$1$	$23.141$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(2\)	\(-1\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots\)
2898.2.a.s	$2898$	$2$	2898.a	1.a	$1$	$1$	$1$	$23.141$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(2\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}+q^{7}+q^{8}+2q^{10}+\cdots\)
2898.2.a.t	$2898$	$2$	2898.a	1.a	$1$	$1$	$1$	$23.141$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(3\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}+3q^{10}+\cdots\)
2898.2.a.u	$2898$	$2$	2898.a	1.a	$1$	$1$	$1$	$23.141$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(4\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+4q^{5}+q^{7}+q^{8}+4q^{10}+\cdots\)
2898.2.a.v	$2898$	$2$	2898.a	1.a	$1$	$2$	$2$	$23.141$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(-2\)	\(0\)	\(-4\)	\(2\)		$+$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-2q^{5}+q^{7}-q^{8}+2q^{10}+\cdots\)
2898.2.a.w	$2898$	$2$	2898.a	1.a	$1$	$2$	$2$	$23.141$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-2\)	\(2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1+\beta )q^{5}+q^{7}-q^{8}+\cdots\)
2898.2.a.x	$2898$	$2$	2898.a	1.a	$1$	$2$	$2$	$23.141$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(3\)	\(-2\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(1+\beta )q^{5}-q^{7}-q^{8}+\cdots\)
2898.2.a.y	$2898$	$2$	2898.a	1.a	$1$	$2$	$2$	$23.141$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(4\)	\(-2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(2+\beta )q^{5}-q^{7}-q^{8}+\cdots\)
2898.2.a.z	$2898$	$2$	2898.a	1.a	$1$	$2$	$2$	$23.141$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(2\)	\(0\)	\(-4\)	\(-2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-2+\beta )q^{5}-q^{7}+q^{8}+\cdots\)
2898.2.a.ba	$2898$	$2$	2898.a	1.a	$1$	$2$	$2$	$23.141$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(2\)	\(0\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta q^{5}-q^{7}+q^{8}-\beta q^{10}+\cdots\)
2898.2.a.bb	$2898$	$2$	2898.a	1.a	$1$	$2$	$2$	$23.141$	\(\Q(\sqrt{41}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(-1\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta q^{5}+q^{7}+q^{8}-\beta q^{10}+\cdots\)
2898.2.a.bc	$2898$	$2$	2898.a	1.a	$1$	$2$	$2$	$23.141$	\(\Q(\sqrt{41}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta q^{5}-q^{7}+q^{8}+\beta q^{10}+\cdots\)
2898.2.a.bd	$2898$	$2$	2898.a	1.a	$1$	$2$	$2$	$23.141$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(1+\beta )q^{5}-q^{7}+q^{8}+\cdots\)
2898.2.a.be	$2898$	$2$	2898.a	1.a	$1$	$3$	$3$	$23.141$	3.3.316.1	None	✓	$1$	$1$	\(-3\)	\(0\)	\(-4\)	\(-3\)		$+$	$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1+\beta _{2})q^{5}-q^{7}-q^{8}+\cdots\)
2898.2.a.bf	$2898$	$2$	2898.a	1.a	$1$	$3$	$3$	$23.141$	3.3.568.1	None	✓	$1$	$0$	\(-3\)	\(0\)	\(-1\)	\(-3\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta _{2}q^{5}-q^{7}-q^{8}-\beta _{2}q^{10}+\cdots\)
2898.2.a.bg	$2898$	$2$	2898.a	1.a	$1$	$3$	$3$	$23.141$	3.3.568.1	None	✓	$1$	$0$	\(3\)	\(0\)	\(1\)	\(-3\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta _{2}q^{5}-q^{7}+q^{8}-\beta _{2}q^{10}+\cdots\)
2898.2.a.bh	$2898$	$2$	2898.a	1.a	$1$	$4$	$4$	$23.141$	4.4.271296.1	None	✓	$1$	$0$	\(-4\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta _{1}q^{5}+q^{7}-q^{8}-\beta _{1}q^{10}+\cdots\)
2898.2.a.bi	$2898$	$2$	2898.a	1.a	$1$	$4$	$4$	$23.141$	4.4.271296.1	None	✓	$1$	$0$	\(4\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-\beta _{1}q^{5}+q^{7}+q^{8}-\beta _{1}q^{10}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2898))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2898)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(207))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(414))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(483))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(966))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1449))\)\(^{\oplus 2}\)