Space of modular forms of level 8, weight 13, and Character 8.d

• Label: 8.13.d
• Level: $8$
• Weight: $13$
• Character orbit: 8.d
• Rep. character: $\chi_{8}(3,\cdot)$
• Character field: $\Q$
• Dimension: $11$
• Newform subspaces: $2$
• Sturm bound: $13$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(13\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(8, [\chi])\).

	Total	New	Old
Modular forms	13	13	0
Cusp forms	11	11	0
Eisenstein series	2	2	0

Trace form

11 * q - 46 * q^2 - 2 * q^3 + 1652 * q^4 - 88676 * q^6 + 289304 * q^8 + 1594321 * q^9 + 1873200 * q^10 - 2668322 * q^11 - 2732552 * q^12 + 12728736 * q^14 - 21516784 * q^16 - 2419562 * q^17 + 1926742 * q^18 - 51868610 * q^19 + 17615520 * q^20 - 103924772 * q^22 + 341593744 * q^24 - 462805765 * q^25 + 151295184 * q^26 + 967927996 * q^27 - 132075840 * q^28 + 456064800 * q^30 - 1577462176 * q^32 + 787396076 * q^33 + 1555715044 * q^34 - 2838470400 * q^35 - 4478101220 * q^36 - 3983433572 * q^38 + 8180322240 * q^40 - 3710988362 * q^41 + 14692585920 * q^42 + 18050876638 * q^43 - 20073482120 * q^44 - 16813594656 * q^46 + 24349522528 * q^48 - 25691199637 * q^49 + 40513425650 * q^50 + 6952490492 * q^51 - 36172521120 * q^52 - 100535014088 * q^54 + 154450364544 * q^56 + 22549744556 * q^57 + 193270394640 * q^58 - 100809712226 * q^59 - 347360715840 * q^60 - 299237961600 * q^62 + 344932668992 * q^64 + 96485235840 * q^65 + 567267337352 * q^66 + 125184923518 * q^67 - 482345621912 * q^68 - 799057954560 * q^70 + 1051757829832 * q^72 - 9696103562 * q^73 + 742739480496 * q^74 - 91148212130 * q^75 - 1059904664072 * q^76 - 1795838526240 * q^78 + 1981932232320 * q^80 + 39118873879 * q^81 + 2206318374628 * q^82 - 339177211202 * q^83 - 3144240693120 * q^84 - 2711857667492 * q^86 + 2674492705168 * q^88 + 47015069110 * q^89 + 3983485096080 * q^90 + 361546645248 * q^91 - 2649411172800 * q^92 - 2517413216064 * q^94 + 3543110668864 * q^96 + 182261693398 * q^97 + 3263732873234 * q^98 - 906543916678 * q^99

Decomposition of \(S_{13}^{\mathrm{new}}(8, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
8.13.d.a	$8$	$13$	8.d	8.d	$2$	$1$	$1$	$7.312$	\(\Q\)	\(\Q(\sqrt{-2}) \)	✓	✓			8.13.d.a	$2$	$0$	\(64\)	\(658\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{6}q^{2}+658q^{3}+2^{12}q^{4}+42112q^{6}+\cdots\)
8.13.d.b	$8$	$13$	8.d	8.d	$2$	$10$	$10$	$7.312$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		✓	✓		8.13.d.b	$2$	$0$	\(-110\)	\(-660\)	\(0\)	\(0\)	$2^{45}\cdot 3^{3}\cdot 23$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-11-\beta _{1})q^{2}+(-66+3\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)