Space of modular forms of level 2254, weight 4, and trivial character

• Label: 2254.4.a
• Level: $2254$
• Weight: $4$
• Character orbit: 2254.a
• Rep. character: $\chi_{2254}(1,\cdot)$
• Character field: $\Q$
• Dimension: $226$
• Newform subspaces: $29$
• Sturm bound: $1344$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2254 = 2 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2254.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 29 \)
Sturm bound:			\(1344\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2254))\).

	Total	New	Old
Modular forms	1024	226	798
Cusp forms	992	226	766
Eisenstein series	32	0	32

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

\(2\)	\(7\)	\(23\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(29\)
\(+\)	\(+\)	\(-\)	\(-\)	\(25\)
\(+\)	\(-\)	\(+\)	\(-\)	\(28\)
\(+\)	\(-\)	\(-\)	\(+\)	\(31\)
\(-\)	\(+\)	\(+\)	\(-\)	\(27\)
\(-\)	\(+\)	\(-\)	\(+\)	\(31\)
\(-\)	\(-\)	\(+\)	\(+\)	\(29\)
\(-\)	\(-\)	\(-\)	\(-\)	\(26\)
Plus space			\(+\)	\(120\)
Minus space			\(-\)	\(106\)

Trace form

226 * q + 4 * q^3 + 904 * q^4 - 10 * q^5 - 32 * q^6 + 1998 * q^9 + 28 * q^10 - 66 * q^11 + 16 * q^12 + 36 * q^13 - 4 * q^15 + 3616 * q^16 - 172 * q^17 - 128 * q^18 + 142 * q^19 - 40 * q^20 + 260 * q^22 - 128 * q^24 + 5410 * q^25 - 120 * q^26 + 4 * q^27 + 612 * q^29 + 144 * q^30 + 636 * q^31 - 308 * q^33 - 520 * q^34 + 7992 * q^36 + 2030 * q^37 + 60 * q^38 + 2124 * q^39 + 112 * q^40 - 492 * q^41 + 866 * q^43 - 264 * q^44 + 730 * q^45 + 92 * q^46 + 676 * q^47 + 64 * q^48 + 1384 * q^50 + 2284 * q^51 + 144 * q^52 + 1858 * q^53 - 992 * q^54 + 1552 * q^55 + 1096 * q^57 - 520 * q^58 + 764 * q^59 - 16 * q^60 - 546 * q^61 + 1200 * q^62 + 14464 * q^64 - 376 * q^65 - 608 * q^66 - 4174 * q^67 - 688 * q^68 - 276 * q^69 + 676 * q^71 - 512 * q^72 - 1676 * q^73 - 2452 * q^74 + 1700 * q^75 + 568 * q^76 - 2848 * q^78 - 5788 * q^79 - 160 * q^80 + 18274 * q^81 - 376 * q^82 - 510 * q^83 - 2004 * q^85 - 1692 * q^86 + 3348 * q^87 + 1040 * q^88 + 4316 * q^89 + 4300 * q^90 - 10236 * q^93 + 1440 * q^94 - 4128 * q^95 - 512 * q^96 - 972 * q^97 + 1978 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2254))\) 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	7	23
2254.4.a.a	$2254$	$4$	2254.a	1.a	$1$	$1$	$1$	$132.990$	\(\Q\)	None	✓				46.4.a.a	$1$	$0$	\(-2\)	\(1\)	\(10\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+q^{3}+4q^{4}+10q^{5}-2q^{6}+\cdots\)
2254.4.a.b	$2254$	$4$	2254.a	1.a	$1$	$1$	$1$	$132.990$	\(\Q\)	None	✓				46.4.a.b	$1$	$0$	\(2\)	\(9\)	\(20\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+9q^{3}+4q^{4}+20q^{5}+18q^{6}+\cdots\)
2254.4.a.c	$2254$	$4$	2254.a	1.a	$1$	$2$	$2$	$132.990$	\(\Q(\sqrt{73}) \)	None	✓				322.4.a.b	$1$	$0$	\(-4\)	\(-9\)	\(8\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(-4-\beta )q^{3}+4q^{4}+(6-4\beta )q^{5}+\cdots\)
2254.4.a.d	$2254$	$4$	2254.a	1.a	$1$	$2$	$2$	$132.990$	\(\Q(\sqrt{41}) \)	None	✓				46.4.a.c	$1$	$1$	\(-4\)	\(1\)	\(-10\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(-1+3\beta )q^{3}+4q^{4}+(-4+\cdots)q^{5}+\cdots\)
2254.4.a.e	$2254$	$4$	2254.a	1.a	$1$	$2$	$2$	$132.990$	\(\Q(\sqrt{2}) \)	None	✓				322.4.a.a	$1$	$0$	\(-4\)	\(4\)	\(-16\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(2+3\beta )q^{3}+4q^{4}+(-8-3\beta )q^{5}+\cdots\)
2254.4.a.f	$2254$	$4$	2254.a	1.a	$1$	$2$	$2$	$132.990$	\(\Q(\sqrt{73}) \)	None	✓				46.4.a.d	$1$	$1$	\(4\)	\(-3\)	\(-10\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-1-\beta )q^{3}+4q^{4}+(-6+\cdots)q^{5}+\cdots\)
2254.4.a.g	$2254$	$4$	2254.a	1.a	$1$	$2$	$2$	$132.990$	\(\Q(\sqrt{57}) \)	None	✓				322.4.a.c	$1$	$1$	\(4\)	\(-1\)	\(18\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-\beta q^{3}+4q^{4}+(8+2\beta )q^{5}+\cdots\)
2254.4.a.h	$2254$	$4$	2254.a	1.a	$1$	$3$	$3$	$132.990$	3.3.15384.1	None	✓				322.4.a.d	$1$	$1$	\(-6\)	\(3\)	\(-8\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(-3-2\beta _{1}+\cdots)q^{5}+\cdots\)
2254.4.a.i	$2254$	$4$	2254.a	1.a	$1$	$3$	$3$	$132.990$	3.3.3368.1	None	✓				322.4.a.e	$1$	$0$	\(6\)	\(7\)	\(8\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+2q^{2}+(2+\beta _{2})q^{3}+4q^{4}+(3-\beta _{1}+\cdots)q^{5}+\cdots\)
2254.4.a.j	$2254$	$4$	2254.a	1.a	$1$	$4$	$4$	$132.990$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				322.4.a.f	$1$	$1$	\(-8\)	\(1\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+\beta _{1}q^{3}+4q^{4}+\beta _{2}q^{5}-2\beta _{1}q^{6}+\cdots\)
2254.4.a.k	$2254$	$4$	2254.a	1.a	$1$	$5$	$5$	$132.990$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				322.4.a.g	$1$	$0$	\(-10\)	\(9\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q-2q^{2}+(2-\beta _{4})q^{3}+4q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
2254.4.a.l	$2254$	$4$	2254.a	1.a	$1$	$5$	$5$	$132.990$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				322.4.a.h	$1$	$1$	\(10\)	\(-5\)	\(-22\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(-4+\cdots)q^{5}+\cdots\)
2254.4.a.m	$2254$	$4$	2254.a	1.a	$1$	$6$	$6$	$132.990$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓				322.4.a.i	$1$	$0$	\(12\)	\(-13\)	\(-12\)	\(0\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-2-\beta _{1})q^{3}+4q^{4}+(-2+\cdots)q^{5}+\cdots\)
2254.4.a.n	$2254$	$4$	2254.a	1.a	$1$	$6$	$6$	$132.990$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓			2254.4.a.n	$2$	$1$	\(12\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+2q^{2}+\beta _{5}q^{3}+4q^{4}-\beta _{3}q^{5}+2\beta _{5}q^{6}+\cdots\)
2254.4.a.o	$2254$	$4$	2254.a	1.a	$1$	$8$	$8$	$132.990$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓			2254.4.a.o	$2$	$1$	\(-16\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$+$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q-2q^{2}+\beta _{1}q^{3}+4q^{4}+\beta _{6}q^{5}-2\beta _{1}q^{6}+\cdots\)
2254.4.a.p	$2254$	$4$	2254.a	1.a	$1$	$8$	$8$	$132.990$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓			2254.4.a.p	$2$	$0$	\(16\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$2^{8}$	$\mathrm{SU}(2)$	\(q+2q^{2}+\beta _{1}q^{3}+4q^{4}+(\beta _{1}+\beta _{5})q^{5}+\cdots\)
2254.4.a.q	$2254$	$4$	2254.a	1.a	$1$	$10$	$10$	$132.990$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓			2254.4.a.q	$2$	$0$	\(-20\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$2^{7}$	$\mathrm{SU}(2)$	\(q-2q^{2}+\beta _{1}q^{3}+4q^{4}+(-\beta _{1}+\beta _{7}+\cdots)q^{5}+\cdots\)
2254.4.a.r	$2254$	$4$	2254.a	1.a	$1$	$11$	$11$	$132.990$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓				322.4.e.d	$1$	$1$	\(-22\)	\(0\)	\(-23\)	\(0\)		$+$	$+$	$-$	$-$	$7$	$\mathrm{SU}(2)$	\(q-2q^{2}-\beta _{1}q^{3}+4q^{4}+(-2-\beta _{2}+\cdots)q^{5}+\cdots\)
2254.4.a.s	$2254$	$4$	2254.a	1.a	$1$	$11$	$11$	$132.990$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓		✓		322.4.e.c	$1$	$1$	\(-22\)	\(0\)	\(-17\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+\beta _{1}q^{3}+4q^{4}+(-2+\beta _{3}+\cdots)q^{5}+\cdots\)
2254.4.a.t	$2254$	$4$	2254.a	1.a	$1$	$11$	$11$	$132.990$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓				322.4.e.c	$1$	$0$	\(-22\)	\(0\)	\(17\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-\beta _{1}q^{3}+4q^{4}+(2-\beta _{3})q^{5}+\cdots\)
2254.4.a.u	$2254$	$4$	2254.a	1.a	$1$	$11$	$11$	$132.990$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓		✓		322.4.e.d	$1$	$0$	\(-22\)	\(0\)	\(23\)	\(0\)		$+$	$-$	$-$	$+$	$7$	$\mathrm{SU}(2)$	\(q-2q^{2}+\beta _{1}q^{3}+4q^{4}+(2+\beta _{2})q^{5}+\cdots\)
2254.4.a.v	$2254$	$4$	2254.a	1.a	$1$	$11$	$11$	$132.990$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓		✓		322.4.e.a	$1$	$1$	\(22\)	\(-18\)	\(-33\)	\(0\)		$-$	$-$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-2+\beta _{1})q^{3}+4q^{4}+(-3+\cdots)q^{5}+\cdots\)
2254.4.a.w	$2254$	$4$	2254.a	1.a	$1$	$11$	$11$	$132.990$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓				322.4.e.b	$1$	$1$	\(22\)	\(-6\)	\(-27\)	\(0\)		$-$	$+$	$+$	$-$	$3$	$\mathrm{SU}(2)$	\(q+2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(-2+\cdots)q^{5}+\cdots\)
2254.4.a.x	$2254$	$4$	2254.a	1.a	$1$	$11$	$11$	$132.990$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓		✓		322.4.e.b	$1$	$0$	\(22\)	\(6\)	\(27\)	\(0\)		$-$	$-$	$+$	$+$	$3$	$\mathrm{SU}(2)$	\(q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(2+\beta _{4}+\cdots)q^{5}+\cdots\)
2254.4.a.y	$2254$	$4$	2254.a	1.a	$1$	$11$	$11$	$132.990$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓				322.4.e.a	$1$	$0$	\(22\)	\(18\)	\(33\)	\(0\)		$-$	$+$	$-$	$+$	$3$	$\mathrm{SU}(2)$	\(q+2q^{2}+(2-\beta _{1})q^{3}+4q^{4}+(3+\beta _{1}+\cdots)q^{5}+\cdots\)
2254.4.a.z	$2254$	$4$	2254.a	1.a	$1$	$14$	$14$	$132.990$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	✓	✓		2254.4.a.z	$2$	$1$	\(-28\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$-$	$-$	$2^{2}\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q-2q^{2}+\beta _{1}q^{3}+4q^{4}+(-\beta _{1}-\beta _{11}+\cdots)q^{5}+\cdots\)
2254.4.a.ba	$2254$	$4$	2254.a	1.a	$1$	$16$	$16$	$132.990$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	✓	✓		2254.4.a.ba	$2$	$1$	\(32\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$2^{4}\cdot 3^{2}\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q+2q^{2}+\beta _{1}q^{3}+4q^{4}+(-\beta _{1}-\beta _{10}+\cdots)q^{5}+\cdots\)
2254.4.a.bb	$2254$	$4$	2254.a	1.a	$1$	$18$	$18$	$132.990$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	✓	✓		2254.4.a.bb	$2$	$0$	\(-36\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$2^{6}\cdot 7^{4}$	$\mathrm{SU}(2)$	\(q-2q^{2}+\beta _{1}q^{3}+4q^{4}+(\beta _{1}-\beta _{11}+\cdots)q^{5}+\cdots\)
2254.4.a.bc	$2254$	$4$	2254.a	1.a	$1$	$20$	$20$	$132.990$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓	✓		2254.4.a.bc	$2$	$0$	\(40\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$2^{9}\cdot 5^{2}\cdot 7^{4}$	$\mathrm{SU}(2)$	\(q+2q^{2}+\beta _{1}q^{3}+4q^{4}+(\beta _{1}+\beta _{12}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2254))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2254)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(1127))\)\(^{\oplus 2}\)