Space of modular forms of level 8, weight 24, and trivial character

• Label: 8.24.a
• Level: $8$
• Weight: $24$
• Character orbit: 8.a
• Rep. character: $\chi_{8}(1,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	8.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_0(8))\).

	Total	New	Old
Modular forms	25	6	19
Cusp forms	21	6	15
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.

\(2\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(13\)	\(3\)	\(10\)		\(11\)	\(3\)	\(8\)		\(2\)	\(0\)	\(2\)
\(-\)		\(12\)	\(3\)	\(9\)		\(10\)	\(3\)	\(7\)		\(2\)	\(0\)	\(2\)

Trace form

6 * q - 181240 * q^3 + 127109268 * q^5 - 7654887600 * q^7 + 175899141022 * q^9 + 11979380952 * q^11 + 5184237699300 * q^13 - 24820079438992 * q^15 - 32394005650260 * q^17 - 70562996989272 * q^19 + 853496382998976 * q^21 + 1021687250350320 * q^23 + 2401150459756554 * q^25 - 43565488118812720 * q^27 + 29258183498479236 * q^29 + 220252994095113024 * q^31 - 344307832043818720 * q^33 - 211920045751163808 * q^35 + 1643216350558889940 * q^37 - 3598251155703043792 * q^39 + 943204443062674716 * q^41 + 3057055129607886360 * q^43 + 17561576563658255332 * q^45 - 49934714768142216480 * q^47 + 56658452057086753974 * q^49 - 83825257731785387120 * q^51 + 142927210667858201460 * q^53 - 314287676417730902832 * q^55 + 702700099440164243680 * q^57 - 851897892280699498824 * q^59 + 1140063356341147716036 * q^61 - 2474339153923520876400 * q^63 + 3300481149107569247736 * q^65 - 4246038096274294053240 * q^67 + 6974203168075078558016 * q^69 - 7294791997863670202928 * q^71 + 7304406245664753353820 * q^73 - 9767692663111805759816 * q^75 + 7591249768471030474560 * q^77 - 5849893848182182293984 * q^79 + 11745812036123766767734 * q^81 - 16051898590817645044440 * q^83 - 9981058421586510352920 * q^85 + 44004033094948617908400 * q^87 - 19518654578924261596932 * q^89 + 71745976965039626585568 * q^91 - 198752185431376092811520 * q^93 + 152639371423537591594032 * q^95 - 235066045757732688424500 * q^97 + 454242251758517089155640 * q^99

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_0(8))\) 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
8.24.a.a	$8$	$24$	8.a	1.a	$1$	$3$	$3$	$26.816$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓	✓	8.24.a.a	$1$	$1$	\(0\)	\(-213948\)	\(95628618\)	\(-8647912920\)		$-$	$-$	$2^{21}\cdot 3^{3}$	$\mathrm{SU}(2)$	\(q+(-71316-\beta _{1})q^{3}+(31876206+\cdots)q^{5}+\cdots\)
8.24.a.b	$8$	$24$	8.a	1.a	$1$	$3$	$3$	$26.816$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓	✓	8.24.a.b	$1$	$0$	\(0\)	\(32708\)	\(31480650\)	\(993025320\)		$+$	$+$	$2^{21}\cdot 3\cdot 5$	$\mathrm{SU}(2)$	\(q+(10903+\beta _{1})q^{3}+(10493544-19\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_0(8))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_0(8)) \simeq \) \(S_{24}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{24}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)