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Properties

Label 6675.2
Level 6675
Weight 2
Dimension 1091094
Nonzero newspaces 56
Sturm bound 6336000

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Defining parameters

Level: \( N \) = \( 6675 = 3 \cdot 5^{2} \cdot 89 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 56 \)
Sturm bound: \(6336000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6675))\).

Total New Old
Modular forms 1593856 1098230 495626
Cusp forms 1574145 1091094 483051
Eisenstein series 19711 7136 12575

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6675))\)

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
6675.2.a \(\chi_{6675}(1, \cdot)\) 6675.2.a.a 1 1
6675.2.a.b 1
6675.2.a.c 1
6675.2.a.d 1
6675.2.a.e 1
6675.2.a.f 1
6675.2.a.g 1
6675.2.a.h 1
6675.2.a.i 1
6675.2.a.j 1
6675.2.a.k 2
6675.2.a.l 3
6675.2.a.m 3
6675.2.a.n 3
6675.2.a.o 3
6675.2.a.p 3
6675.2.a.q 4
6675.2.a.r 4
6675.2.a.s 5
6675.2.a.t 5
6675.2.a.u 6
6675.2.a.v 7
6675.2.a.w 7
6675.2.a.x 9
6675.2.a.y 10
6675.2.a.z 10
6675.2.a.ba 10
6675.2.a.bb 12
6675.2.a.bc 12
6675.2.a.bd 15
6675.2.a.be 15
6675.2.a.bf 16
6675.2.a.bg 16
6675.2.a.bh 22
6675.2.a.bi 22
6675.2.a.bj 22
6675.2.a.bk 22
6675.2.c \(\chi_{6675}(5074, \cdot)\) n/a 264 1
6675.2.e \(\chi_{6675}(2224, \cdot)\) n/a 272 1
6675.2.g \(\chi_{6675}(3826, \cdot)\) n/a 284 1
6675.2.j \(\chi_{6675}(1924, \cdot)\) n/a 536 2
6675.2.k \(\chi_{6675}(1568, \cdot)\) n/a 1072 2
6675.2.m \(\chi_{6675}(1868, \cdot)\) n/a 1072 2
6675.2.n \(\chi_{6675}(2582, \cdot)\) n/a 1056 2
6675.2.q \(\chi_{6675}(5018, \cdot)\) n/a 1072 2
6675.2.t \(\chi_{6675}(301, \cdot)\) n/a 572 2
6675.2.u \(\chi_{6675}(1336, \cdot)\) n/a 1760 4
6675.2.w \(\chi_{6675}(101, \cdot)\) n/a 2256 4
6675.2.x \(\chi_{6675}(457, \cdot)\) n/a 1080 4
6675.2.y \(\chi_{6675}(1768, \cdot)\) n/a 1080 4
6675.2.bc \(\chi_{6675}(749, \cdot)\) n/a 2144 4
6675.2.bd \(\chi_{6675}(1156, \cdot)\) n/a 1808 4
6675.2.bg \(\chi_{6675}(1069, \cdot)\) n/a 1760 4
6675.2.bi \(\chi_{6675}(889, \cdot)\) n/a 1792 4
6675.2.bk \(\chi_{6675}(601, \cdot)\) n/a 2840 10
6675.2.bl \(\chi_{6675}(856, \cdot)\) n/a 3584 8
6675.2.bo \(\chi_{6675}(212, \cdot)\) n/a 7168 8
6675.2.br \(\chi_{6675}(713, \cdot)\) n/a 7040 8
6675.2.bs \(\chi_{6675}(533, \cdot)\) n/a 7168 8
6675.2.bu \(\chi_{6675}(767, \cdot)\) n/a 7168 8
6675.2.bv \(\chi_{6675}(34, \cdot)\) n/a 3616 8
6675.2.by \(\chi_{6675}(526, \cdot)\) n/a 2840 10
6675.2.ca \(\chi_{6675}(799, \cdot)\) n/a 2720 10
6675.2.cc \(\chi_{6675}(1024, \cdot)\) n/a 2720 10
6675.2.ce \(\chi_{6675}(344, \cdot)\) n/a 14336 16
6675.2.ci \(\chi_{6675}(37, \cdot)\) n/a 7200 16
6675.2.cj \(\chi_{6675}(838, \cdot)\) n/a 7200 16
6675.2.ck \(\chi_{6675}(611, \cdot)\) n/a 14336 16
6675.2.cm \(\chi_{6675}(376, \cdot)\) n/a 5720 20
6675.2.cp \(\chi_{6675}(68, \cdot)\) n/a 10720 20
6675.2.cs \(\chi_{6675}(32, \cdot)\) n/a 10720 20
6675.2.ct \(\chi_{6675}(443, \cdot)\) n/a 10720 20
6675.2.cv \(\chi_{6675}(1193, \cdot)\) n/a 10720 20
6675.2.cw \(\chi_{6675}(49, \cdot)\) n/a 5360 20
6675.2.cy \(\chi_{6675}(16, \cdot)\) n/a 18080 40
6675.2.cz \(\chi_{6675}(74, \cdot)\) n/a 21440 40
6675.2.dd \(\chi_{6675}(43, \cdot)\) n/a 10800 40
6675.2.de \(\chi_{6675}(7, \cdot)\) n/a 10800 40
6675.2.df \(\chi_{6675}(26, \cdot)\) n/a 22560 40
6675.2.di \(\chi_{6675}(139, \cdot)\) n/a 17920 40
6675.2.dk \(\chi_{6675}(4, \cdot)\) n/a 17920 40
6675.2.dn \(\chi_{6675}(406, \cdot)\) n/a 18080 40
6675.2.dp \(\chi_{6675}(79, \cdot)\) n/a 36160 80
6675.2.dq \(\chi_{6675}(53, \cdot)\) n/a 71680 80
6675.2.ds \(\chi_{6675}(203, \cdot)\) n/a 71680 80
6675.2.dt \(\chi_{6675}(2, \cdot)\) n/a 71680 80
6675.2.dw \(\chi_{6675}(17, \cdot)\) n/a 71680 80
6675.2.dz \(\chi_{6675}(106, \cdot)\) n/a 35840 80
6675.2.eb \(\chi_{6675}(41, \cdot)\) n/a 143360 160
6675.2.ec \(\chi_{6675}(13, \cdot)\) n/a 72000 160
6675.2.ed \(\chi_{6675}(28, \cdot)\) n/a 72000 160
6675.2.eh \(\chi_{6675}(14, \cdot)\) n/a 143360 160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6675))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6675)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(89))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(267))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(445))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1335))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2225))\)\(^{\oplus 2}\)