Space of modular forms of level 152, weight 16, and trivial character

• Label: 152.16.a
• Level: $152$
• Weight: $16$
• Character orbit: 152.a
• Rep. character: $\chi_{152}(1,\cdot)$
• Character field: $\Q$
• Dimension: $67$
• Newform subspaces: $4$
• Sturm bound: $320$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	152.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(320\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_0(152))\).

	Total	New	Old
Modular forms	304	67	237
Cusp forms	296	67	229
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		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(78\)	\(17\)	\(61\)		\(76\)	\(17\)	\(59\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)		\(75\)	\(17\)	\(58\)		\(73\)	\(17\)	\(56\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)		\(74\)	\(15\)	\(59\)		\(72\)	\(15\)	\(57\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)		\(77\)	\(18\)	\(59\)		\(75\)	\(18\)	\(57\)		\(2\)	\(0\)	\(2\)
Plus space		\(+\)		\(155\)	\(35\)	\(120\)		\(151\)	\(35\)	\(116\)		\(4\)	\(0\)	\(4\)
Minus space		\(-\)		\(149\)	\(32\)	\(117\)		\(145\)	\(32\)	\(113\)		\(4\)	\(0\)	\(4\)

Trace form

67 * q + 157584 * q^5 - 3173532 * q^7 + 312167125 * q^9 + 116923026 * q^11 + 117253446 * q^13 - 1483539528 * q^15 - 3593986066 * q^17 + 2681615217 * q^19 - 21543587520 * q^21 + 22154919402 * q^23 + 288743884499 * q^25 + 285363817920 * q^27 - 213041217118 * q^29 + 333817683276 * q^31 - 478462084924 * q^33 + 956121311298 * q^35 - 780546753658 * q^37 + 821647579590 * q^39 - 234515553222 * q^41 + 3091055895354 * q^43 + 9152136928092 * q^45 - 16735173351570 * q^47 + 55149018754095 * q^49 - 39436411788372 * q^51 + 38426477589974 * q^53 - 8231330292186 * q^55 - 3909794986386 * q^57 - 8595549967400 * q^59 - 54021140397356 * q^61 - 19227916497530 * q^63 + 50019198177424 * q^65 + 60650098655372 * q^67 - 370200757484612 * q^69 + 135878553747640 * q^71 - 232213568258302 * q^73 + 70021370365076 * q^75 + 39530414117482 * q^77 + 242910313871436 * q^79 + 2008460785779699 * q^81 + 105609714798632 * q^83 + 1363960387723730 * q^85 - 1728255873313370 * q^87 + 348200109632922 * q^89 - 235637976012896 * q^91 - 604751397539396 * q^93 + 330719156453946 * q^97 + 5900209684900862 * q^99

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_0(152))\) 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
152.16.a.a	$152$	$16$	152.a	1.a	$1$	$15$	$15$	$216.894$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	✓	✓	✓	152.16.a.a	$1$	$1$	\(0\)	\(-2395\)	\(-139593\)	\(-2691324\)		$-$	$+$	$-$	$2^{75}\cdot 3^{8}\cdot 5^{4}$	$\mathrm{SU}(2)$	\(q+(-160+\beta _{1})q^{3}+(-9307+3\beta _{1}+\cdots)q^{5}+\cdots\)
152.16.a.b	$152$	$16$	152.a	1.a	$1$	$17$	$17$	$216.894$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	✓	✓	✓	152.16.a.b	$1$	$1$	\(0\)	\(-1979\)	\(140260\)	\(-3013157\)		$+$	$-$	$-$	$2^{93}\cdot 3^{6}\cdot 5^{3}\cdot 7$	$\mathrm{SU}(2)$	\(q+(-116-\beta _{1})q^{3}+(8249+4\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
152.16.a.c	$152$	$16$	152.a	1.a	$1$	$17$	$17$	$216.894$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	✓	✓	✓	152.16.a.c	$1$	$0$	\(0\)	\(4582\)	\(218385\)	\(1928101\)		$+$	$+$	$+$	$2^{91}\cdot 3^{9}\cdot 5^{6}\cdot 7$	$\mathrm{SU}(2)$	\(q+(270-\beta _{1})q^{3}+(12845+3\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
152.16.a.d	$152$	$16$	152.a	1.a	$1$	$18$	$18$	$216.894$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	✓	✓	✓	152.16.a.d	$1$	$0$	\(0\)	\(-208\)	\(-61468\)	\(602848\)		$-$	$-$	$+$	$2^{104}\cdot 3^{5}\cdot 5^{6}$	$\mathrm{SU}(2)$	\(q+(-12+\beta _{1})q^{3}+(-3414-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_0(152))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_0(152)) \simeq \) \(S_{16}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 2}\)