↑

Properties

Label 86.6
Level 86
Weight 6
Dimension 385
Nonzero newspaces 4
Newform subspaces 10
Sturm bound 2772
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 86 = 2 \cdot 43 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 10 \)
Sturm bound: \(2772\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(86))\).

Total New Old
Modular forms 1197 385 812
Cusp forms 1113 385 728
Eisenstein series 84 0 84

Trace form

\( 385 q + O(q^{10}) \) \( 385 q + 60886 q^{31} - 30996 q^{33} - 80388 q^{34} - 127596 q^{35} - 72576 q^{36} - 65604 q^{37} - 10416 q^{38} + 53802 q^{39} + 65478 q^{41} + 148176 q^{42} + 361410 q^{43} + 59808 q^{44} + 187110 q^{45} + 13776 q^{46} - 29022 q^{47} - 235298 q^{49} - 252336 q^{50} - 271404 q^{51} - 162176 q^{52} - 150276 q^{53} + 20412 q^{54} + 310884 q^{55} + 215586 q^{57} + 726810 q^{69} + 71778 q^{71} - 229782 q^{73} - 1010625 q^{75} - 599634 q^{77} - 83580 q^{79} + 492072 q^{81} + 496356 q^{83} + 606900 q^{85} + 1373610 q^{87} + 328020 q^{89} - 21084 q^{91} - 858648 q^{93} - 795900 q^{95} - 1481634 q^{97} - 1469265 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(86))\)

We only show spaces with even 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
86.6.a \(\chi_{86}(1, \cdot)\) 86.6.a.a 3 1
86.6.a.b 3
86.6.a.c 5
86.6.a.d 6
86.6.c \(\chi_{86}(49, \cdot)\) 86.6.c.a 18 2
86.6.c.b 20
86.6.e \(\chi_{86}(11, \cdot)\) 86.6.e.a 48 6
86.6.e.b 54
86.6.g \(\chi_{86}(9, \cdot)\) 86.6.g.a 108 12
86.6.g.b 120

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(86))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(86)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 2}\)