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Properties

Label 8464.2
Level 8464
Weight 2
Dimension 1248986
Nonzero newspaces 16
Sturm bound 8937984

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Defining parameters

Level: \( N \) = \( 8464 = 2^{4} \cdot 23^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(8937984\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8464))\).

Total New Old
Modular forms 2244968 1255327 989641
Cusp forms 2224025 1248986 975039
Eisenstein series 20943 6341 14602

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8464))\)

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
8464.2.a \(\chi_{8464}(1, \cdot)\) 8464.2.a.a 1 1
8464.2.a.b 1
8464.2.a.c 1
8464.2.a.d 1
8464.2.a.e 1
8464.2.a.f 1
8464.2.a.g 1
8464.2.a.h 1
8464.2.a.i 1
8464.2.a.j 1
8464.2.a.k 1
8464.2.a.l 1
8464.2.a.m 1
8464.2.a.n 1
8464.2.a.o 1
8464.2.a.p 1
8464.2.a.q 1
8464.2.a.r 1
8464.2.a.s 1
8464.2.a.t 2
8464.2.a.u 2
8464.2.a.v 2
8464.2.a.w 2
8464.2.a.x 2
8464.2.a.y 2
8464.2.a.z 2
8464.2.a.ba 2
8464.2.a.bb 2
8464.2.a.bc 2
8464.2.a.bd 2
8464.2.a.be 2
8464.2.a.bf 2
8464.2.a.bg 2
8464.2.a.bh 2
8464.2.a.bi 2
8464.2.a.bj 2
8464.2.a.bk 3
8464.2.a.bl 4
8464.2.a.bm 4
8464.2.a.bn 4
8464.2.a.bo 4
8464.2.a.bp 4
8464.2.a.bq 4
8464.2.a.br 4
8464.2.a.bs 5
8464.2.a.bt 5
8464.2.a.bu 5
8464.2.a.bv 5
8464.2.a.bw 5
8464.2.a.bx 5
8464.2.a.by 6
8464.2.a.bz 6
8464.2.a.ca 8
8464.2.a.cb 8
8464.2.a.cc 8
8464.2.a.cd 10
8464.2.a.ce 10
8464.2.a.cf 12
8464.2.a.cg 15
8464.2.a.ch 15
8464.2.a.ci 15
8464.2.a.cj 15
8464.2.b \(\chi_{8464}(4233, \cdot)\) None 0 1
8464.2.c \(\chi_{8464}(8463, \cdot)\) n/a 252 1
8464.2.h \(\chi_{8464}(4231, \cdot)\) None 0 1
8464.2.i \(\chi_{8464}(2115, \cdot)\) n/a 1976 2
8464.2.j \(\chi_{8464}(2117, \cdot)\) n/a 1978 2
8464.2.m \(\chi_{8464}(177, \cdot)\) n/a 2420 10
8464.2.n \(\chi_{8464}(263, \cdot)\) None 0 10
8464.2.s \(\chi_{8464}(63, \cdot)\) n/a 2520 10
8464.2.t \(\chi_{8464}(1545, \cdot)\) None 0 10
8464.2.u \(\chi_{8464}(369, \cdot)\) n/a 6050 22
8464.2.x \(\chi_{8464}(501, \cdot)\) n/a 19760 20
8464.2.y \(\chi_{8464}(195, \cdot)\) n/a 19760 20
8464.2.z \(\chi_{8464}(183, \cdot)\) None 0 22
8464.2.be \(\chi_{8464}(367, \cdot)\) n/a 6072 22
8464.2.bf \(\chi_{8464}(185, \cdot)\) None 0 22
8464.2.bi \(\chi_{8464}(93, \cdot)\) n/a 48488 44
8464.2.bj \(\chi_{8464}(91, \cdot)\) n/a 48488 44
8464.2.bk \(\chi_{8464}(49, \cdot)\) n/a 60500 220
8464.2.bl \(\chi_{8464}(9, \cdot)\) None 0 220
8464.2.bm \(\chi_{8464}(15, \cdot)\) n/a 60720 220
8464.2.br \(\chi_{8464}(7, \cdot)\) None 0 220
8464.2.bs \(\chi_{8464}(11, \cdot)\) n/a 484880 440
8464.2.bt \(\chi_{8464}(13, \cdot)\) n/a 484880 440

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8464))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8464)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(529))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1058))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2116))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4232))\)\(^{\oplus 2}\)