Properties

Label 80.18
Level 80
Weight 18
Dimension 1670
Nonzero newspaces 7
Sturm bound 6912
Trace bound 3

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Defining parameters

Level: \( N \) = \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) = \( 18 \)
Nonzero newspaces: \( 7 \)
Sturm bound: \(6912\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(80))\).

Total New Old
Modular forms 3320 1696 1624
Cusp forms 3208 1670 1538
Eisenstein series 112 26 86

Trace form

\( 1670 q - 4 q^{2} + 13118 q^{3} + 109480 q^{4} + 12232 q^{5} + 19318800 q^{6} - 26311046 q^{7} + 203064464 q^{8} - 762404052 q^{9} - 284165332 q^{10} + 1259492528 q^{11} - 1294602640 q^{12} + 4770833750 q^{13}+ \cdots - 46\!\cdots\!04 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(80))\)

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
80.18.a \(\chi_{80}(1, \cdot)\) 80.18.a.a 1 1
80.18.a.b 2
80.18.a.c 2
80.18.a.d 2
80.18.a.e 2
80.18.a.f 2
80.18.a.g 3
80.18.a.h 3
80.18.a.i 4
80.18.a.j 4
80.18.a.k 4
80.18.a.l 5
80.18.c \(\chi_{80}(49, \cdot)\) 80.18.c.a 8 1
80.18.c.b 8
80.18.c.c 8
80.18.c.d 26
80.18.d \(\chi_{80}(41, \cdot)\) None 0 1
80.18.f \(\chi_{80}(9, \cdot)\) None 0 1
80.18.j \(\chi_{80}(43, \cdot)\) n/a 404 2
80.18.l \(\chi_{80}(21, \cdot)\) n/a 272 2
80.18.n \(\chi_{80}(47, \cdot)\) n/a 102 2
80.18.o \(\chi_{80}(7, \cdot)\) None 0 2
80.18.q \(\chi_{80}(29, \cdot)\) n/a 404 2
80.18.s \(\chi_{80}(3, \cdot)\) n/a 404 2

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(80))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(80)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 5}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)