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Properties

Label 4050.2
Level 4050
Weight 2
Dimension 106176
Nonzero newspaces 24
Sturm bound 1749600

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Defining parameters

Level: \( N \) = \( 4050 = 2 \cdot 3^{4} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(1749600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4050))\).

Total New Old
Modular forms 443448 106176 337272
Cusp forms 431353 106176 325177
Eisenstein series 12095 0 12095

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4050))\)

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
4050.2.a \(\chi_{4050}(1, \cdot)\) 4050.2.a.a 1 1
4050.2.a.b 1
4050.2.a.c 1
4050.2.a.d 1
4050.2.a.e 1
4050.2.a.f 1
4050.2.a.g 1
4050.2.a.h 1
4050.2.a.i 1
4050.2.a.j 1
4050.2.a.k 1
4050.2.a.l 1
4050.2.a.m 1
4050.2.a.n 1
4050.2.a.o 1
4050.2.a.p 1
4050.2.a.q 1
4050.2.a.r 1
4050.2.a.s 1
4050.2.a.t 1
4050.2.a.u 1
4050.2.a.v 1
4050.2.a.w 1
4050.2.a.x 1
4050.2.a.y 1
4050.2.a.z 1
4050.2.a.ba 1
4050.2.a.bb 1
4050.2.a.bc 1
4050.2.a.bd 1
4050.2.a.be 1
4050.2.a.bf 1
4050.2.a.bg 1
4050.2.a.bh 1
4050.2.a.bi 1
4050.2.a.bj 1
4050.2.a.bk 2
4050.2.a.bl 2
4050.2.a.bm 2
4050.2.a.bn 2
4050.2.a.bo 2
4050.2.a.bp 2
4050.2.a.bq 2
4050.2.a.br 2
4050.2.a.bs 2
4050.2.a.bt 2
4050.2.a.bu 2
4050.2.a.bv 2
4050.2.a.bw 2
4050.2.a.bx 2
4050.2.a.by 2
4050.2.a.bz 2
4050.2.a.ca 4
4050.2.a.cb 4
4050.2.c \(\chi_{4050}(649, \cdot)\) 4050.2.c.a 2 1
4050.2.c.b 2
4050.2.c.c 2
4050.2.c.d 2
4050.2.c.e 2
4050.2.c.f 2
4050.2.c.g 2
4050.2.c.h 2
4050.2.c.i 2
4050.2.c.j 2
4050.2.c.k 2
4050.2.c.l 2
4050.2.c.m 2
4050.2.c.n 2
4050.2.c.o 2
4050.2.c.p 2
4050.2.c.q 2
4050.2.c.r 2
4050.2.c.s 2
4050.2.c.t 2
4050.2.c.u 4
4050.2.c.v 4
4050.2.c.w 4
4050.2.c.x 4
4050.2.c.y 4
4050.2.c.z 4
4050.2.c.ba 4
4050.2.c.bb 4
4050.2.e \(\chi_{4050}(1351, \cdot)\) n/a 152 2
4050.2.f \(\chi_{4050}(1457, \cdot)\) n/a 144 2
4050.2.h \(\chi_{4050}(811, \cdot)\) n/a 480 4
4050.2.j \(\chi_{4050}(1999, \cdot)\) n/a 144 2
4050.2.l \(\chi_{4050}(451, \cdot)\) n/a 342 6
4050.2.m \(\chi_{4050}(1459, \cdot)\) n/a 480 4
4050.2.q \(\chi_{4050}(107, \cdot)\) n/a 288 4
4050.2.r \(\chi_{4050}(271, \cdot)\) n/a 960 8
4050.2.u \(\chi_{4050}(199, \cdot)\) n/a 324 6
4050.2.w \(\chi_{4050}(323, \cdot)\) n/a 960 8
4050.2.x \(\chi_{4050}(151, \cdot)\) n/a 3078 18
4050.2.ba \(\chi_{4050}(109, \cdot)\) n/a 960 8
4050.2.bc \(\chi_{4050}(143, \cdot)\) n/a 648 12
4050.2.bd \(\chi_{4050}(91, \cdot)\) n/a 2160 24
4050.2.bg \(\chi_{4050}(49, \cdot)\) n/a 2916 18
4050.2.bh \(\chi_{4050}(53, \cdot)\) n/a 1920 16
4050.2.bj \(\chi_{4050}(19, \cdot)\) n/a 2160 24
4050.2.bm \(\chi_{4050}(257, \cdot)\) n/a 5832 36
4050.2.bo \(\chi_{4050}(31, \cdot)\) n/a 19440 72
4050.2.bp \(\chi_{4050}(17, \cdot)\) n/a 4320 48
4050.2.br \(\chi_{4050}(79, \cdot)\) n/a 19440 72
4050.2.bv \(\chi_{4050}(23, \cdot)\) n/a 38880 144

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4050))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4050)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(270))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(405))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(675))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(810))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1350))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2025))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4050))\)\(^{\oplus 1}\)