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Properties

Label 7500.2
Level 7500
Weight 2
Dimension 603264
Nonzero newspaces 24
Sturm bound 6000000

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Defining parameters

Level: \( N \) = \( 7500 = 2^{2} \cdot 3 \cdot 5^{4} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(6000000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7500))\).

Total New Old
Modular forms 1511000 606336 904664
Cusp forms 1489001 603264 885737
Eisenstein series 21999 3072 18927

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7500))\)

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
7500.2.a \(\chi_{7500}(1, \cdot)\) 7500.2.a.a 4 1
7500.2.a.b 4
7500.2.a.c 4
7500.2.a.d 4
7500.2.a.e 4
7500.2.a.f 4
7500.2.a.g 4
7500.2.a.h 4
7500.2.a.i 4
7500.2.a.j 4
7500.2.a.k 8
7500.2.a.l 8
7500.2.a.m 12
7500.2.a.n 12
7500.2.d \(\chi_{7500}(1249, \cdot)\) 7500.2.d.a 8 1
7500.2.d.b 8
7500.2.d.c 8
7500.2.d.d 8
7500.2.d.e 8
7500.2.d.f 16
7500.2.d.g 24
7500.2.e \(\chi_{7500}(6251, \cdot)\) n/a 928 1
7500.2.h \(\chi_{7500}(7499, \cdot)\) n/a 928 1
7500.2.i \(\chi_{7500}(2057, \cdot)\) n/a 320 2
7500.2.j \(\chi_{7500}(3307, \cdot)\) n/a 960 2
7500.2.m \(\chi_{7500}(1501, \cdot)\) n/a 320 4
7500.2.n \(\chi_{7500}(251, \cdot)\) n/a 3744 4
7500.2.o \(\chi_{7500}(2749, \cdot)\) n/a 320 4
7500.2.r \(\chi_{7500}(1499, \cdot)\) n/a 3744 4
7500.2.w \(\chi_{7500}(307, \cdot)\) n/a 3840 8
7500.2.x \(\chi_{7500}(557, \cdot)\) n/a 1280 8
7500.2.y \(\chi_{7500}(301, \cdot)\) n/a 1520 20
7500.2.bb \(\chi_{7500}(299, \cdot)\) n/a 17760 20
7500.2.bc \(\chi_{7500}(49, \cdot)\) n/a 1480 20
7500.2.bf \(\chi_{7500}(551, \cdot)\) n/a 17760 20
7500.2.bh \(\chi_{7500}(7, \cdot)\) n/a 18000 40
7500.2.bi \(\chi_{7500}(257, \cdot)\) n/a 6000 40
7500.2.bk \(\chi_{7500}(61, \cdot)\) n/a 12400 100
7500.2.bl \(\chi_{7500}(11, \cdot)\) n/a 149600 100
7500.2.bo \(\chi_{7500}(59, \cdot)\) n/a 149600 100
7500.2.bp \(\chi_{7500}(109, \cdot)\) n/a 12600 100
7500.2.bu \(\chi_{7500}(67, \cdot)\) n/a 150000 200
7500.2.bv \(\chi_{7500}(17, \cdot)\) n/a 50000 200

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7500))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7500)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(250))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(375))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(500))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(625))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(750))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1250))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1500))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1875))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2500))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3750))\)\(^{\oplus 2}\)