Space of modular forms of level 8 and weight 13

• Label: 8.13
• Level: 8
• Weight: 13
• Dimension: 11
• Nonzero newspaces: 1
• Newform subspaces: 2
• Sturm bound: 52
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 8 = 2^{3} \)
Weight:	\( k \)	=	\( 13 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 2 \)
Sturm bound:			\(52\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(\Gamma_1(8))\).

	Total	New	Old
Modular forms	27	13	14
Cusp forms	21	11	10
Eisenstein series	6	2	4

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 \(S_{13}^{\mathrm{new}}(\Gamma_1(8))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
8.13.c	\(\chi_{8}(7, \cdot)\)	None	0	1
8.13.d	\(\chi_{8}(3, \cdot)\)	8.13.d.a	1	1
		8.13.d.b	10

Decomposition of \(S_{13}^{\mathrm{old}}(\Gamma_1(8))\) into lower level spaces

\( S_{13}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{13}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)