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Properties

Label 6936.2
Level 6936
Weight 2
Dimension 556461
Nonzero newspaces 30
Sturm bound 5326848

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Defining parameters

Level: \( N \) = \( 6936 = 2^{3} \cdot 3 \cdot 17^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(5326848\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6936))\).

Total New Old
Modular forms 1341312 559409 781903
Cusp forms 1322113 556461 765652
Eisenstein series 19199 2948 16251

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6936))\)

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
6936.2.a \(\chi_{6936}(1, \cdot)\) 6936.2.a.a 1 1
6936.2.a.b 1
6936.2.a.c 1
6936.2.a.d 1
6936.2.a.e 1
6936.2.a.f 1
6936.2.a.g 1
6936.2.a.h 1
6936.2.a.i 1
6936.2.a.j 1
6936.2.a.k 1
6936.2.a.l 1
6936.2.a.m 1
6936.2.a.n 1
6936.2.a.o 1
6936.2.a.p 1
6936.2.a.q 1
6936.2.a.r 2
6936.2.a.s 2
6936.2.a.t 2
6936.2.a.u 2
6936.2.a.v 2
6936.2.a.w 2
6936.2.a.x 2
6936.2.a.y 2
6936.2.a.z 2
6936.2.a.ba 2
6936.2.a.bb 3
6936.2.a.bc 3
6936.2.a.bd 3
6936.2.a.be 3
6936.2.a.bf 6
6936.2.a.bg 6
6936.2.a.bh 6
6936.2.a.bi 6
6936.2.a.bj 6
6936.2.a.bk 6
6936.2.a.bl 8
6936.2.a.bm 8
6936.2.a.bn 8
6936.2.a.bo 8
6936.2.a.bp 9
6936.2.a.bq 9
6936.2.c \(\chi_{6936}(577, \cdot)\) n/a 134 1
6936.2.e \(\chi_{6936}(6359, \cdot)\) None 0 1
6936.2.f \(\chi_{6936}(3469, \cdot)\) n/a 542 1
6936.2.h \(\chi_{6936}(3467, \cdot)\) n/a 1052 1
6936.2.j \(\chi_{6936}(2891, \cdot)\) n/a 1054 1
6936.2.l \(\chi_{6936}(4045, \cdot)\) n/a 540 1
6936.2.o \(\chi_{6936}(6935, \cdot)\) None 0 1
6936.2.q \(\chi_{6936}(251, \cdot)\) n/a 2104 2
6936.2.s \(\chi_{6936}(829, \cdot)\) n/a 1080 2
6936.2.v \(\chi_{6936}(3217, \cdot)\) n/a 268 2
6936.2.x \(\chi_{6936}(2639, \cdot)\) None 0 2
6936.2.ba \(\chi_{6936}(3289, \cdot)\) n/a 544 4
6936.2.bb \(\chi_{6936}(2711, \cdot)\) None 0 4
6936.2.bc \(\chi_{6936}(733, \cdot)\) n/a 2160 4
6936.2.bd \(\chi_{6936}(155, \cdot)\) n/a 4208 4
6936.2.bh \(\chi_{6936}(65, \cdot)\) n/a 2160 8
6936.2.bi \(\chi_{6936}(1231, \cdot)\) None 0 8
6936.2.bl \(\chi_{6936}(643, \cdot)\) n/a 4320 8
6936.2.bm \(\chi_{6936}(653, \cdot)\) n/a 8416 8
6936.2.bo \(\chi_{6936}(409, \cdot)\) n/a 2464 16
6936.2.bq \(\chi_{6936}(407, \cdot)\) None 0 16
6936.2.bt \(\chi_{6936}(373, \cdot)\) n/a 9792 16
6936.2.bv \(\chi_{6936}(35, \cdot)\) n/a 19520 16
6936.2.bx \(\chi_{6936}(203, \cdot)\) n/a 19520 16
6936.2.bz \(\chi_{6936}(205, \cdot)\) n/a 9792 16
6936.2.ca \(\chi_{6936}(239, \cdot)\) None 0 16
6936.2.cc \(\chi_{6936}(169, \cdot)\) n/a 2464 16
6936.2.ce \(\chi_{6936}(47, \cdot)\) None 0 32
6936.2.cg \(\chi_{6936}(217, \cdot)\) n/a 4928 32
6936.2.cj \(\chi_{6936}(13, \cdot)\) n/a 19584 32
6936.2.cl \(\chi_{6936}(395, \cdot)\) n/a 39040 32
6936.2.co \(\chi_{6936}(59, \cdot)\) n/a 78080 64
6936.2.cp \(\chi_{6936}(229, \cdot)\) n/a 39168 64
6936.2.cq \(\chi_{6936}(263, \cdot)\) None 0 64
6936.2.cr \(\chi_{6936}(25, \cdot)\) n/a 9728 64
6936.2.cv \(\chi_{6936}(5, \cdot)\) n/a 156160 128
6936.2.cw \(\chi_{6936}(91, \cdot)\) n/a 78336 128
6936.2.cz \(\chi_{6936}(7, \cdot)\) None 0 128
6936.2.da \(\chi_{6936}(41, \cdot)\) n/a 39168 128

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6936))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6936)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(408))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(578))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(867))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1734))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2312))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3468))\)\(^{\oplus 2}\)