Space of modular forms of level 119, weight 4, and trivial character

• Label: 119.4.a
• Level: $119$
• Weight: $4$
• Character orbit: 119.a
• Rep. character: $\chi_{119}(1,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $5$
• Sturm bound: $48$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 119 = 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	119.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(48\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(119))\).

	Total	New	Old
Modular forms	38	24	14
Cusp forms	34	24	10
Eisenstein series	4	0	4

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

\(7\)	\(17\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(13\)	\(8\)	\(5\)		\(12\)	\(8\)	\(4\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)		\(6\)	\(3\)	\(3\)		\(5\)	\(3\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(8\)	\(4\)	\(4\)		\(7\)	\(4\)	\(3\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(11\)	\(9\)	\(2\)		\(10\)	\(9\)	\(1\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(24\)	\(17\)	\(7\)		\(22\)	\(17\)	\(5\)		\(2\)	\(0\)	\(2\)
Minus space		\(-\)		\(14\)	\(7\)	\(7\)		\(12\)	\(7\)	\(5\)		\(2\)	\(0\)	\(2\)

Trace form

24 * q + 2 * q^2 + 8 * q^3 + 86 * q^4 - 16 * q^5 + 60 * q^6 + 14 * q^7 - 30 * q^8 + 152 * q^9 + 144 * q^10 + 68 * q^11 + 20 * q^12 + 48 * q^13 - 14 * q^14 - 40 * q^15 + 310 * q^16 + 210 * q^18 - 24 * q^19 + 432 * q^20 - 232 * q^22 + 16 * q^23 + 1188 * q^24 + 856 * q^25 - 16 * q^26 + 200 * q^27 - 98 * q^28 + 804 * q^29 - 546 * q^30 + 32 * q^31 - 528 * q^32 - 40 * q^33 - 56 * q^35 - 1936 * q^36 + 12 * q^37 - 1092 * q^38 - 584 * q^39 - 964 * q^40 + 360 * q^41 - 70 * q^42 + 132 * q^43 - 112 * q^44 + 256 * q^45 + 216 * q^46 - 1608 * q^47 - 3080 * q^48 + 1176 * q^49 - 1588 * q^50 + 408 * q^51 + 732 * q^52 + 584 * q^53 - 1628 * q^54 - 56 * q^55 + 210 * q^56 + 960 * q^57 + 1520 * q^58 - 1392 * q^59 - 3334 * q^60 + 1056 * q^61 - 4064 * q^62 - 434 * q^63 + 2182 * q^64 - 64 * q^65 - 3376 * q^66 + 620 * q^67 + 472 * q^69 + 504 * q^70 + 1000 * q^71 - 1080 * q^72 - 136 * q^73 - 204 * q^74 + 1184 * q^75 + 1780 * q^76 - 952 * q^77 - 996 * q^78 + 2720 * q^79 + 64 * q^80 + 1584 * q^81 - 2660 * q^82 + 2512 * q^83 - 476 * q^85 - 2782 * q^86 - 600 * q^87 + 2980 * q^88 + 4128 * q^89 + 332 * q^90 + 728 * q^91 - 5176 * q^92 - 2464 * q^93 + 2676 * q^94 + 2936 * q^95 + 748 * q^96 - 488 * q^97 + 98 * q^98 + 6212 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(119))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		7	17
119.4.a.a	$119$	$4$	119.a	1.a	$1$	$1$	$1$	$7.021$	\(\Q\)	None	✓	✓			119.4.a.a	$1$	$0$	\(-1\)	\(-6\)	\(-20\)	\(-7\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-6q^{3}-7q^{4}-20q^{5}+6q^{6}+\cdots\)
119.4.a.b	$119$	$4$	119.a	1.a	$1$	$3$	$3$	$7.021$	3.3.2429.1	None	✓	✓	✓	✓	119.4.a.b	$1$	$1$	\(-1\)	\(5\)	\(-19\)	\(-21\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1}-\beta _{2})q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots\)
119.4.a.c	$119$	$4$	119.a	1.a	$1$	$4$	$4$	$7.021$	4.4.68557.1	None	✓	✓	✓	✓	119.4.a.c	$1$	$1$	\(-2\)	\(-7\)	\(-9\)	\(28\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(-2-\beta _{1}-\beta _{3})q^{3}+\cdots\)
119.4.a.d	$119$	$4$	119.a	1.a	$1$	$7$	$7$	$7.021$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓		119.4.a.d	$1$	$0$	\(4\)	\(5\)	\(35\)	\(-49\)		$+$	$+$	$+$	$3$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-\beta _{2}-\beta _{3})q^{3}+(7+\cdots)q^{4}+\cdots\)
119.4.a.e	$119$	$4$	119.a	1.a	$1$	$9$	$9$	$7.021$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓	✓	✓	119.4.a.e	$1$	$0$	\(2\)	\(11\)	\(-3\)	\(63\)		$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{5})q^{3}+(4+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(119))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(119)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 2}\)