Space of modular forms of level 5148, weight 2, and trivial character

• Label: 5148.2.a
• Level: $5148$
• Weight: $2$
• Character orbit: 5148.a
• Rep. character: $\chi_{5148}(1,\cdot)$
• Character field: $\Q$
• Dimension: $50$
• Newform subspaces: $20$
• Sturm bound: $2016$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 5148 = 2^{2} \cdot 3^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5148.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 20 \)
Sturm bound:			\(2016\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5148))\).

	Total	New	Old
Modular forms	1032	50	982
Cusp forms	985	50	935
Eisenstein series	47	0	47

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

\(2\)	\(3\)	\(11\)	\(13\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(5\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(5\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(5\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(5\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(8\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(8\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(7\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(7\)
Plus space				\(+\)	\(25\)
Minus space				\(-\)	\(25\)

Trace form

\( 50 q - 2 q^{5} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5148))\) 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	13
5148.2.a.a	$5148$	$2$	5148.a	1.a	$1$	$1$	$1$	$41.107$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}+2q^{7}-q^{11}+q^{13}+2q^{19}+\cdots\)
5148.2.a.b	$5148$	$2$	5148.a	1.a	$1$	$1$	$1$	$41.107$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{11}+q^{13}+6q^{17}+4q^{23}+\cdots\)
5148.2.a.c	$5148$	$2$	5148.a	1.a	$1$	$1$	$1$	$41.107$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+q^{11}+q^{13}+2q^{17}+6q^{19}+\cdots\)
5148.2.a.d	$5148$	$2$	5148.a	1.a	$1$	$1$	$1$	$41.107$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}+q^{11}+q^{13}-6q^{17}+2q^{19}+\cdots\)
5148.2.a.e	$5148$	$2$	5148.a	1.a	$1$	$1$	$1$	$41.107$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-2q^{7}-q^{11}+q^{13}+2q^{19}+\cdots\)
5148.2.a.f	$5148$	$2$	5148.a	1.a	$1$	$1$	$1$	$41.107$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{11}+q^{13}-6q^{17}-4q^{23}+\cdots\)
5148.2.a.g	$5148$	$2$	5148.a	1.a	$1$	$2$	$2$	$41.107$	\(\Q(\sqrt{21}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(5\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+(2+\beta )q^{7}+q^{11}-q^{13}+4q^{17}+\cdots\)
5148.2.a.h	$5148$	$2$	5148.a	1.a	$1$	$2$	$2$	$41.107$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-3\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{7}+q^{11}+q^{13}+2\beta q^{17}+\cdots\)
5148.2.a.i	$5148$	$2$	5148.a	1.a	$1$	$2$	$2$	$41.107$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}-q^{11}-q^{13}+(1-3\beta )q^{17}+\cdots\)
5148.2.a.j	$5148$	$2$	5148.a	1.a	$1$	$2$	$2$	$41.107$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(2+\beta )q^{5}+2\beta q^{7}+q^{11}-q^{13}+\cdots\)
5148.2.a.k	$5148$	$2$	5148.a	1.a	$1$	$2$	$2$	$41.107$	\(\Q(\sqrt{21}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(3\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+(2-\beta )q^{7}-q^{11}+q^{13}+(-3+\cdots)q^{19}+\cdots\)
5148.2.a.l	$5148$	$2$	5148.a	1.a	$1$	$3$	$3$	$41.107$	3.3.404.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-4\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-2\beta _{1}+\beta _{2})q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots\)
5148.2.a.m	$5148$	$2$	5148.a	1.a	$1$	$3$	$3$	$41.107$	3.3.564.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(4\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{5}+(1-\beta _{2})q^{7}-q^{11}+\cdots\)
5148.2.a.n	$5148$	$2$	5148.a	1.a	$1$	$3$	$3$	$41.107$	3.3.1620.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{5}+\beta _{2}q^{7}+q^{11}-q^{13}+(-2+\cdots)q^{17}+\cdots\)
5148.2.a.o	$5148$	$2$	5148.a	1.a	$1$	$3$	$3$	$41.107$	3.3.229.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-7\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{5}+(-2-2\beta _{1}+\beta _{2})q^{7}+\cdots\)
5148.2.a.p	$5148$	$2$	5148.a	1.a	$1$	$4$	$4$	$41.107$	4.4.82128.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+\cdots\)
5148.2.a.q	$5148$	$2$	5148.a	1.a	$1$	$4$	$4$	$41.107$	4.4.90996.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}+(1+\beta _{2})q^{7}-q^{11}+q^{13}+\cdots\)
5148.2.a.r	$5148$	$2$	5148.a	1.a	$1$	$4$	$4$	$41.107$	4.4.82128.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+q^{11}+\cdots\)
5148.2.a.s	$5148$	$2$	5148.a	1.a	$1$	$5$	$5$	$41.107$	5.5.815952.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{5}+\beta _{3}q^{7}+q^{11}-q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots\)
5148.2.a.t	$5148$	$2$	5148.a	1.a	$1$	$5$	$5$	$41.107$	5.5.815952.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{4}q^{5}+\beta _{3}q^{7}-q^{11}-q^{13}+(\beta _{1}+\cdots)q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5148))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5148)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(396))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(429))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(468))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(572))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(858))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1287))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1716))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2574))\)\(^{\oplus 2}\)