Space of modular forms of level 13, weight 11, and Character 13.d

• Label: 13.11.d
• Level: $13$
• Weight: $11$
• Character orbit: 13.d
• Rep. character: $\chi_{13}(5,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	13.d (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(13, [\chi])\).

	Total	New	Old
Modular forms	24	24	0
Cusp forms	20	20	0
Eisenstein series	4	4	0

Trace form

20 * q - 34 * q^2 - 4 * q^3 - 7792 * q^5 - 19264 * q^6 - 38312 * q^7 - 1200 * q^8 + 236192 * q^9 + 331856 * q^11 - 445380 * q^13 + 2007244 * q^14 + 379412 * q^15 - 1736492 * q^16 - 5990914 * q^18 - 2277428 * q^19 + 3611836 * q^20 - 9480856 * q^21 + 5001216 * q^22 + 41307672 * q^24 + 6769646 * q^26 - 4427116 * q^27 - 113669380 * q^28 + 37095424 * q^29 + 17376308 * q^31 - 1963204 * q^32 - 118752028 * q^33 - 32678040 * q^34 + 283757932 * q^35 + 138434576 * q^37 - 180959428 * q^39 - 8799876 * q^40 - 431088064 * q^41 + 1089534556 * q^42 + 102766076 * q^44 - 551620384 * q^45 - 682329276 * q^46 - 316356304 * q^47 - 332833468 * q^48 + 653613022 * q^50 - 1360524100 * q^52 + 882722032 * q^53 + 206912984 * q^54 - 1205505576 * q^55 + 2161977296 * q^57 + 450412980 * q^58 + 1130230868 * q^59 + 4118247964 * q^60 - 1735259352 * q^61 - 3186516460 * q^63 + 2833033736 * q^65 + 1165082704 * q^66 - 626922128 * q^67 - 11230951788 * q^68 - 3144181512 * q^70 - 196931776 * q^71 + 614552052 * q^72 + 5765831656 * q^73 + 10475267944 * q^74 - 5350301912 * q^76 + 8069244872 * q^78 + 1110987384 * q^79 + 870087872 * q^80 - 21624920380 * q^81 + 13391403584 * q^83 - 25726991224 * q^84 + 1992219096 * q^85 + 32878542048 * q^86 + 194656048 * q^87 + 5940615128 * q^89 + 670762144 * q^91 - 12619717320 * q^92 - 27707434216 * q^93 - 31866209148 * q^94 + 34182859808 * q^96 - 14392811236 * q^97 - 58567835410 * q^98 + 64175005436 * q^99

Decomposition of \(S_{11}^{\mathrm{new}}(13, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
13.11.d.a	$13$	$11$	13.d	13.d	$4$	$20$	$10$	$8.260$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓	✓	13.11.d.a	$2$	$0$	\(-34\)	\(-4\)	\(-7792\)	\(-38312\)	$2^{20}\cdot 3^{6}\cdot 13^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2-2\beta _{2}+\beta _{3})q^{2}+(-\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)