Space of modular forms of level 1872, weight 2, and trivial character

• Label: 1872.2.a
• Level: $1872$
• Weight: $2$
• Character orbit: 1872.a
• Rep. character: $\chi_{1872}(1,\cdot)$
• Character field: $\Q$
• Dimension: $30$
• Newform subspaces: $25$
• Sturm bound: $672$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1872.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 25 \)
Sturm bound:			\(672\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1872))\).

	Total	New	Old
Modular forms	360	30	330
Cusp forms	313	30	283
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.

\(2\)	\(3\)	\(13\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(42\)	\(2\)	\(40\)		\(37\)	\(2\)	\(35\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)		\(46\)	\(4\)	\(42\)		\(40\)	\(4\)	\(36\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(48\)	\(5\)	\(43\)		\(42\)	\(5\)	\(37\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(44\)	\(4\)	\(40\)		\(38\)	\(4\)	\(34\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(48\)	\(4\)	\(44\)		\(42\)	\(4\)	\(38\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(44\)	\(2\)	\(42\)		\(38\)	\(2\)	\(36\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(42\)	\(4\)	\(38\)		\(36\)	\(4\)	\(32\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(46\)	\(5\)	\(41\)		\(40\)	\(5\)	\(35\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(172\)	\(12\)	\(160\)		\(149\)	\(12\)	\(137\)		\(23\)	\(0\)	\(23\)
Minus space			\(-\)		\(188\)	\(18\)	\(170\)		\(164\)	\(18\)	\(146\)		\(24\)	\(0\)	\(24\)

Trace form

30 * q - 2 * q^7 - 10 * q^11 + 4 * q^17 + 14 * q^19 + 8 * q^23 + 38 * q^25 + 16 * q^29 + 2 * q^31 + 8 * q^37 - 4 * q^41 + 4 * q^43 - 14 * q^47 + 38 * q^49 + 4 * q^53 + 20 * q^55 - 18 * q^59 - 20 * q^61 - 10 * q^67 + 22 * q^71 - 4 * q^73 + 4 * q^77 + 4 * q^79 + 26 * q^83 - 4 * q^89 + 6 * q^91 - 36 * q^95 - 20 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1872))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	13
1872.2.a.a	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	\(\Q\)	None	✓				468.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-4q^{7}-4q^{11}-q^{13}-8q^{23}+\cdots\)
1872.2.a.b	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	\(\Q\)	None	✓				312.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-2q^{11}-q^{13}-2q^{17}-8q^{19}+\cdots\)
1872.2.a.c	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	\(\Q\)	None	✓				78.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-4q^{7}-4q^{11}+q^{13}-2q^{17}+\cdots\)
1872.2.a.d	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	\(\Q\)	None	✓				936.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{7}+4q^{11}-q^{13}+2q^{19}+\cdots\)
1872.2.a.e	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	\(\Q\)	None	✓				312.2.a.f	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+q^{13}-2q^{17}+4q^{19}-q^{25}+\cdots\)
1872.2.a.f	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	\(\Q\)	None	✓				52.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+2q^{7}-2q^{11}-q^{13}-6q^{17}+\cdots\)
1872.2.a.g	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	\(\Q\)	None	✓				234.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+2q^{7}+4q^{11}-q^{13}+6q^{19}+\cdots\)
1872.2.a.h	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	\(\Q\)	None	✓				39.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+4q^{7}+4q^{11}+q^{13}-2q^{17}+\cdots\)
1872.2.a.i	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	\(\Q\)	None	✓				156.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+q^{13}+6q^{17}-2q^{19}-5q^{25}+\cdots\)
1872.2.a.j	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	\(\Q\)	None	✓				312.2.a.e	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+6q^{11}-q^{13}-2q^{17}+4q^{23}-5q^{25}+\cdots\)
1872.2.a.k	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	\(\Q\)	None	✓				312.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}-2q^{11}-q^{13}+6q^{17}+4q^{19}+\cdots\)
1872.2.a.l	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	\(\Q\)	None	✓				104.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-5q^{7}-2q^{11}-q^{13}+3q^{17}+\cdots\)
1872.2.a.m	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	\(\Q\)	None	✓				26.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-2q^{11}-q^{13}+3q^{17}+\cdots\)
1872.2.a.n	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	\(\Q\)	None	✓				312.2.a.a	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-4q^{7}+q^{13}-2q^{17}-8q^{19}+\cdots\)
1872.2.a.o	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	\(\Q\)	None	✓				936.2.a.c	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-2q^{7}-4q^{11}-q^{13}+2q^{19}+\cdots\)
1872.2.a.p	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	\(\Q\)	None	✓				234.2.a.a	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2q^{7}-4q^{11}-q^{13}+6q^{19}+\cdots\)
1872.2.a.q	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	\(\Q\)	None	✓				26.2.a.a	$1$	$0$	\(0\)	\(0\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+q^{7}+6q^{11}+q^{13}+3q^{17}+\cdots\)
1872.2.a.r	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	\(\Q\)	None	✓				468.2.a.a	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}-4q^{7}+4q^{11}-q^{13}+8q^{23}+\cdots\)
1872.2.a.s	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	\(\Q\)	None	✓				156.2.a.a	$1$	$0$	\(0\)	\(0\)	\(4\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+2q^{7}-4q^{11}+q^{13}-2q^{17}+\cdots\)
1872.2.a.t	$1872$	$2$	1872.a	1.a	$1$	$1$	$1$	$14.948$	\(\Q\)	None	✓				312.2.a.d	$1$	$0$	\(0\)	\(0\)	\(4\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+4q^{7}-2q^{11}-q^{13}+6q^{17}+\cdots\)
1872.2.a.u	$1872$	$2$	1872.a	1.a	$1$	$2$	$2$	$14.948$	\(\Q(\sqrt{17}) \)	None	✓		✓		104.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}+(1-\beta )q^{7}+(-2+2\beta )q^{11}+\cdots\)
1872.2.a.v	$1872$	$2$	1872.a	1.a	$1$	$2$	$2$	$14.948$	\(\Q(\sqrt{3}) \)	None	✓		✓	✓	117.2.a.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-2q^{7}-\beta q^{11}+q^{13}+2\beta q^{17}-2q^{19}+\cdots\)
1872.2.a.w	$1872$	$2$	1872.a	1.a	$1$	$2$	$2$	$14.948$	\(\Q(\sqrt{2}) \)	None	✓		✓		39.2.a.b	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}-\beta q^{7}-2q^{11}-q^{13}+(-2+\cdots)q^{17}+\cdots\)
1872.2.a.x	$1872$	$2$	1872.a	1.a	$1$	$2$	$2$	$14.948$	\(\Q(\sqrt{2}) \)	None	✓				936.2.a.k	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(2-\beta )q^{7}+(-2+\beta )q^{11}+\cdots\)
1872.2.a.y	$1872$	$2$	1872.a	1.a	$1$	$2$	$2$	$14.948$	\(\Q(\sqrt{2}) \)	None	✓				936.2.a.k	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(2+\beta )q^{7}+(2+\beta )q^{11}+q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1872))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1872)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(468))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(624))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(936))\)\(^{\oplus 2}\)