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Properties

Label 8304.2
Level 8304
Weight 2
Dimension 806462
Nonzero newspaces 28
Sturm bound 7661568

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Defining parameters

Level: \( N \) = \( 8304 = 2^{4} \cdot 3 \cdot 173 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 28 \)
Sturm bound: \(7661568\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8304))\).

Total New Old
Modular forms 1925024 809542 1115482
Cusp forms 1905761 806462 1099299
Eisenstein series 19263 3080 16183

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8304))\)

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
8304.2.a \(\chi_{8304}(1, \cdot)\) 8304.2.a.a 1 1
8304.2.a.b 1
8304.2.a.c 1
8304.2.a.d 1
8304.2.a.e 1
8304.2.a.f 1
8304.2.a.g 1
8304.2.a.h 1
8304.2.a.i 2
8304.2.a.j 2
8304.2.a.k 2
8304.2.a.l 2
8304.2.a.m 3
8304.2.a.n 3
8304.2.a.o 3
8304.2.a.p 3
8304.2.a.q 3
8304.2.a.r 3
8304.2.a.s 3
8304.2.a.t 3
8304.2.a.u 3
8304.2.a.v 4
8304.2.a.w 4
8304.2.a.x 4
8304.2.a.y 5
8304.2.a.z 5
8304.2.a.ba 5
8304.2.a.bb 6
8304.2.a.bc 6
8304.2.a.bd 6
8304.2.a.be 6
8304.2.a.bf 7
8304.2.a.bg 7
8304.2.a.bh 7
8304.2.a.bi 10
8304.2.a.bj 11
8304.2.a.bk 11
8304.2.a.bl 12
8304.2.a.bm 13
8304.2.c \(\chi_{8304}(1729, \cdot)\) n/a 174 1
8304.2.e \(\chi_{8304}(6575, \cdot)\) n/a 344 1
8304.2.f \(\chi_{8304}(4153, \cdot)\) None 0 1
8304.2.h \(\chi_{8304}(4151, \cdot)\) None 0 1
8304.2.j \(\chi_{8304}(2423, \cdot)\) None 0 1
8304.2.l \(\chi_{8304}(5881, \cdot)\) None 0 1
8304.2.o \(\chi_{8304}(8303, \cdot)\) n/a 348 1
8304.2.r \(\chi_{8304}(1637, \cdot)\) n/a 2776 2
8304.2.t \(\chi_{8304}(5443, \cdot)\) n/a 1392 2
8304.2.w \(\chi_{8304}(2075, \cdot)\) n/a 2776 2
8304.2.x \(\chi_{8304}(2077, \cdot)\) n/a 1376 2
8304.2.y \(\chi_{8304}(785, \cdot)\) n/a 692 2
8304.2.z \(\chi_{8304}(4591, \cdot)\) n/a 348 2
8304.2.bc \(\chi_{8304}(439, \cdot)\) None 0 2
8304.2.bd \(\chi_{8304}(4937, \cdot)\) None 0 2
8304.2.bg \(\chi_{8304}(347, \cdot)\) n/a 2752 2
8304.2.bh \(\chi_{8304}(3805, \cdot)\) n/a 1392 2
8304.2.bk \(\chi_{8304}(1291, \cdot)\) n/a 1392 2
8304.2.bm \(\chi_{8304}(5789, \cdot)\) n/a 2776 2
8304.2.bo \(\chi_{8304}(337, \cdot)\) n/a 7308 42
8304.2.bq \(\chi_{8304}(383, \cdot)\) n/a 14616 42
8304.2.bt \(\chi_{8304}(25, \cdot)\) None 0 42
8304.2.bv \(\chi_{8304}(23, \cdot)\) None 0 42
8304.2.bx \(\chi_{8304}(167, \cdot)\) None 0 42
8304.2.bz \(\chi_{8304}(169, \cdot)\) None 0 42
8304.2.ca \(\chi_{8304}(47, \cdot)\) n/a 14616 42
8304.2.cc \(\chi_{8304}(49, \cdot)\) n/a 7308 42
8304.2.cf \(\chi_{8304}(221, \cdot)\) n/a 116592 84
8304.2.ch \(\chi_{8304}(19, \cdot)\) n/a 58464 84
8304.2.ck \(\chi_{8304}(13, \cdot)\) n/a 58464 84
8304.2.cl \(\chi_{8304}(83, \cdot)\) n/a 116592 84
8304.2.co \(\chi_{8304}(185, \cdot)\) None 0 84
8304.2.cp \(\chi_{8304}(7, \cdot)\) None 0 84
8304.2.cs \(\chi_{8304}(79, \cdot)\) n/a 14616 84
8304.2.ct \(\chi_{8304}(17, \cdot)\) n/a 29064 84
8304.2.cu \(\chi_{8304}(85, \cdot)\) n/a 58464 84
8304.2.cv \(\chi_{8304}(35, \cdot)\) n/a 116592 84
8304.2.cy \(\chi_{8304}(91, \cdot)\) n/a 58464 84
8304.2.da \(\chi_{8304}(5, \cdot)\) n/a 116592 84

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8304))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8304)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(173))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(346))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(519))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(692))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1038))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1384))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2076))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2768))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8304))\)\(^{\oplus 1}\)