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Properties

Label 4624.2
Level 4624
Weight 2
Dimension 370298
Nonzero newspaces 26
Sturm bound 2663424

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Defining parameters

Level: \( N \) = \( 4624 = 2^{4} \cdot 17^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 26 \)
Sturm bound: \(2663424\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4624))\).

Total New Old
Modular forms 671456 373615 297841
Cusp forms 660257 370298 289959
Eisenstein series 11199 3317 7882

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4624))\)

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
4624.2.a \(\chi_{4624}(1, \cdot)\) 4624.2.a.a 1 1
4624.2.a.b 1
4624.2.a.c 1
4624.2.a.d 1
4624.2.a.e 1
4624.2.a.f 1
4624.2.a.g 2
4624.2.a.h 2
4624.2.a.i 2
4624.2.a.j 2
4624.2.a.k 2
4624.2.a.l 2
4624.2.a.m 2
4624.2.a.n 2
4624.2.a.o 2
4624.2.a.p 2
4624.2.a.q 2
4624.2.a.r 2
4624.2.a.s 2
4624.2.a.t 2
4624.2.a.u 2
4624.2.a.v 2
4624.2.a.w 2
4624.2.a.x 2
4624.2.a.y 2
4624.2.a.z 3
4624.2.a.ba 3
4624.2.a.bb 3
4624.2.a.bc 3
4624.2.a.bd 3
4624.2.a.be 3
4624.2.a.bf 3
4624.2.a.bg 3
4624.2.a.bh 3
4624.2.a.bi 3
4624.2.a.bj 3
4624.2.a.bk 3
4624.2.a.bl 4
4624.2.a.bm 4
4624.2.a.bn 4
4624.2.a.bo 4
4624.2.a.bp 4
4624.2.a.bq 4
4624.2.a.br 6
4624.2.a.bs 6
4624.2.a.bt 12
4624.2.b \(\chi_{4624}(577, \cdot)\) n/a 128 1
4624.2.c \(\chi_{4624}(2313, \cdot)\) None 0 1
4624.2.h \(\chi_{4624}(2889, \cdot)\) None 0 1
4624.2.j \(\chi_{4624}(829, \cdot)\) n/a 1052 2
4624.2.l \(\chi_{4624}(1157, \cdot)\) n/a 1054 2
4624.2.m \(\chi_{4624}(905, \cdot)\) None 0 2
4624.2.o \(\chi_{4624}(1985, \cdot)\) n/a 256 2
4624.2.r \(\chi_{4624}(1733, \cdot)\) n/a 1052 2
4624.2.s \(\chi_{4624}(2061, \cdot)\) n/a 1052 2
4624.2.v \(\chi_{4624}(977, \cdot)\) n/a 512 4
4624.2.w \(\chi_{4624}(733, \cdot)\) n/a 2104 4
4624.2.y \(\chi_{4624}(3045, \cdot)\) n/a 2104 4
4624.2.ba \(\chi_{4624}(1001, \cdot)\) None 0 4
4624.2.bd \(\chi_{4624}(75, \cdot)\) n/a 4208 8
4624.2.bf \(\chi_{4624}(447, \cdot)\) n/a 1080 8
4624.2.bg \(\chi_{4624}(503, \cdot)\) None 0 8
4624.2.bj \(\chi_{4624}(2387, \cdot)\) n/a 4208 8
4624.2.bk \(\chi_{4624}(273, \cdot)\) n/a 2432 16
4624.2.bl \(\chi_{4624}(169, \cdot)\) None 0 16
4624.2.bq \(\chi_{4624}(137, \cdot)\) None 0 16
4624.2.br \(\chi_{4624}(33, \cdot)\) n/a 2432 16
4624.2.bt \(\chi_{4624}(149, \cdot)\) n/a 19520 32
4624.2.bu \(\chi_{4624}(101, \cdot)\) n/a 19520 32
4624.2.bx \(\chi_{4624}(81, \cdot)\) n/a 4864 32
4624.2.bz \(\chi_{4624}(89, \cdot)\) None 0 32
4624.2.ca \(\chi_{4624}(69, \cdot)\) n/a 19520 32
4624.2.cc \(\chi_{4624}(13, \cdot)\) n/a 19520 32
4624.2.cf \(\chi_{4624}(9, \cdot)\) None 0 64
4624.2.ch \(\chi_{4624}(53, \cdot)\) n/a 39040 64
4624.2.cj \(\chi_{4624}(189, \cdot)\) n/a 39040 64
4624.2.ck \(\chi_{4624}(49, \cdot)\) n/a 9728 64
4624.2.cm \(\chi_{4624}(107, \cdot)\) n/a 78080 128
4624.2.cp \(\chi_{4624}(7, \cdot)\) None 0 128
4624.2.cq \(\chi_{4624}(31, \cdot)\) n/a 19584 128
4624.2.cs \(\chi_{4624}(3, \cdot)\) n/a 78080 128

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4624))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4624)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(272))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(578))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1156))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2312))\)\(^{\oplus 2}\)