Properties

Label 234.6
Level 234
Weight 6
Dimension 1969
Nonzero newspaces 15
Sturm bound 18144
Trace bound 11

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Defining parameters

Level: \( N \) = \( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 15 \)
Sturm bound: \(18144\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(234))\).

Total New Old
Modular forms 7752 1969 5783
Cusp forms 7368 1969 5399
Eisenstein series 384 0 384

Trace form

\( 1969 q + 16 q^{2} - 18 q^{3} + 64 q^{4} + 84 q^{5} + 168 q^{6} + 952 q^{7} - 320 q^{8} - 1158 q^{9} - 1068 q^{10} + 1734 q^{11} + 768 q^{12} + 4108 q^{13} + 3584 q^{14} - 5328 q^{15} - 9561 q^{17} - 5136 q^{18}+ \cdots - 125172 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(234))\)

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
234.6.a \(\chi_{234}(1, \cdot)\) 234.6.a.a 1 1
234.6.a.b 1
234.6.a.c 1
234.6.a.d 1
234.6.a.e 1
234.6.a.f 1
234.6.a.g 1
234.6.a.h 2
234.6.a.i 2
234.6.a.j 2
234.6.a.k 2
234.6.a.l 2
234.6.a.m 2
234.6.a.n 3
234.6.a.o 3
234.6.b \(\chi_{234}(181, \cdot)\) 234.6.b.a 2 1
234.6.b.b 2
234.6.b.c 6
234.6.b.d 8
234.6.b.e 12
234.6.e \(\chi_{234}(79, \cdot)\) n/a 120 2
234.6.f \(\chi_{234}(133, \cdot)\) n/a 140 2
234.6.g \(\chi_{234}(61, \cdot)\) n/a 140 2
234.6.h \(\chi_{234}(55, \cdot)\) 234.6.h.a 4 2
234.6.h.b 4
234.6.h.c 6
234.6.h.d 6
234.6.h.e 6
234.6.h.f 8
234.6.h.g 12
234.6.h.h 12
234.6.j \(\chi_{234}(125, \cdot)\) 234.6.j.a 24 2
234.6.j.b 28
234.6.l \(\chi_{234}(127, \cdot)\) 234.6.l.a 12 2
234.6.l.b 12
234.6.l.c 12
234.6.l.d 20
234.6.p \(\chi_{234}(43, \cdot)\) n/a 140 2
234.6.s \(\chi_{234}(121, \cdot)\) n/a 140 2
234.6.t \(\chi_{234}(25, \cdot)\) n/a 140 2
234.6.x \(\chi_{234}(71, \cdot)\) 234.6.x.a 40 4
234.6.x.b 48
234.6.y \(\chi_{234}(11, \cdot)\) n/a 280 4
234.6.z \(\chi_{234}(41, \cdot)\) n/a 280 4
234.6.bd \(\chi_{234}(5, \cdot)\) n/a 280 4

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(234))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(234)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 2}\)