Space of modular forms of level 152, weight 6, and trivial character

• Label: 152.6.a
• Level: $152$
• Weight: $6$
• Character orbit: 152.a
• Rep. character: $\chi_{152}(1,\cdot)$
• Character field: $\Q$
• Dimension: $23$
• Newform subspaces: $5$
• Sturm bound: $120$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	152.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(120\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(152))\).

	Total	New	Old
Modular forms	104	23	81
Cusp forms	96	23	73
Eisenstein series	8	0	8

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

\(2\)	\(19\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(6\)
\(+\)	\(-\)	\(-\)	\(6\)
\(-\)	\(+\)	\(-\)	\(7\)
\(-\)	\(-\)	\(+\)	\(4\)
Plus space		\(+\)	\(10\)
Minus space		\(-\)	\(13\)

Trace form

23 * q + 148 * q^5 - 76 * q^7 + 1645 * q^9 - 726 * q^11 - 1178 * q^13 + 2472 * q^15 + 1974 * q^17 - 1083 * q^19 - 2928 * q^21 + 1914 * q^23 + 13475 * q^25 + 9360 * q^27 + 4042 * q^29 + 11484 * q^31 + 4940 * q^33 - 21414 * q^35 - 7994 * q^37 - 2466 * q^39 + 10202 * q^41 - 302 * q^43 + 51528 * q^45 - 43626 * q^47 + 96075 * q^49 + 29004 * q^51 - 874 * q^53 + 46694 * q^55 + 6498 * q^57 + 56168 * q^59 + 38992 * q^61 - 2546 * q^63 - 24904 * q^65 + 8524 * q^67 + 14452 * q^69 + 96184 * q^71 + 70882 * q^73 - 87484 * q^75 + 6294 * q^77 - 47892 * q^79 + 169767 * q^81 - 176440 * q^83 - 11818 * q^85 - 186962 * q^87 + 47274 * q^89 - 200800 * q^91 + 223108 * q^93 - 347494 * q^97 - 173722 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(152))\) 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	19
152.6.a.a	$152$	$6$	152.a	1.a	$1$	$1$	$1$	$24.378$	\(\Q\)	None	✓	✓			152.6.a.a	$1$	$1$	\(0\)	\(-7\)	\(16\)	\(75\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-7q^{3}+2^{4}q^{5}+75q^{7}-194q^{9}+\cdots\)
152.6.a.b	$152$	$6$	152.a	1.a	$1$	$3$	$3$	$24.378$	3.3.976277.1	None	✓	✓	✓		152.6.a.b	$1$	$1$	\(0\)	\(-7\)	\(58\)	\(-197\)		$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{3}+(20+\beta _{1}+\beta _{2})q^{5}+\cdots\)
152.6.a.c	$152$	$6$	152.a	1.a	$1$	$6$	$6$	$24.378$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓	✓	✓	152.6.a.c	$1$	$1$	\(0\)	\(-4\)	\(-25\)	\(-161\)		$+$	$+$	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(-4-\beta _{3})q^{5}+(-26+\cdots)q^{7}+\cdots\)
152.6.a.d	$152$	$6$	152.a	1.a	$1$	$6$	$6$	$24.378$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓	✓	✓	152.6.a.d	$1$	$0$	\(0\)	\(23\)	\(0\)	\(133\)		$+$	$-$	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q+(4-\beta _{1})q^{3}+(-\beta _{1}-\beta _{3})q^{5}+(23+\cdots)q^{7}+\cdots\)
152.6.a.e	$152$	$6$	152.a	1.a	$1$	$7$	$7$	$24.378$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓	✓	152.6.a.e	$1$	$0$	\(0\)	\(-5\)	\(99\)	\(74\)		$-$	$+$	$-$	$2^{9}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(14+\beta _{1}+\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(152))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(152)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 2}\)