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Properties

Label 3750.2
Level 3750
Weight 2
Dimension 86400
Nonzero newspaces 12
Sturm bound 1500000
Trace bound 4

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Defining parameters

Level: \( N \) = \( 3750 = 2 \cdot 3 \cdot 5^{4} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(1500000\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3750))\).

Total New Old
Modular forms 379400 86400 293000
Cusp forms 370601 86400 284201
Eisenstein series 8799 0 8799

Trace form

\( 86400 q + O(q^{10}) \) \( 86400 q - 40 q^{17} - 10 q^{18} - 80 q^{19} - 40 q^{21} - 80 q^{22} - 80 q^{23} - 20 q^{24} - 40 q^{26} - 40 q^{28} - 80 q^{29} - 80 q^{31} - 10 q^{32} - 40 q^{33} - 50 q^{34} - 10 q^{37} - 40 q^{39} - 40 q^{41} - 80 q^{43} - 80 q^{47} - 90 q^{49} - 60 q^{51} - 90 q^{53} - 80 q^{57} - 80 q^{59} - 40 q^{61} + 60 q^{63} + 60 q^{66} + 140 q^{69} + 100 q^{78} + 80 q^{81} - 40 q^{83} + 60 q^{84} + 60 q^{87} - 10 q^{89} - 80 q^{91} - 20 q^{93} - 40 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3750))\)

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
3750.2.a \(\chi_{3750}(1, \cdot)\) 3750.2.a.a 2 1
3750.2.a.b 2
3750.2.a.c 2
3750.2.a.d 2
3750.2.a.e 2
3750.2.a.f 2
3750.2.a.g 2
3750.2.a.h 2
3750.2.a.i 4
3750.2.a.j 4
3750.2.a.k 4
3750.2.a.l 4
3750.2.a.m 4
3750.2.a.n 4
3750.2.a.o 4
3750.2.a.p 4
3750.2.a.q 4
3750.2.a.r 4
3750.2.a.s 4
3750.2.a.t 4
3750.2.a.u 8
3750.2.a.v 8
3750.2.c \(\chi_{3750}(1249, \cdot)\) 3750.2.c.a 4 1
3750.2.c.b 4
3750.2.c.c 4
3750.2.c.d 4
3750.2.c.e 8
3750.2.c.f 8
3750.2.c.g 8
3750.2.c.h 8
3750.2.c.i 8
3750.2.c.j 8
3750.2.c.k 16
3750.2.e \(\chi_{3750}(443, \cdot)\) n/a 320 2
3750.2.g \(\chi_{3750}(751, \cdot)\) n/a 320 4
3750.2.h \(\chi_{3750}(499, \cdot)\) n/a 320 4
3750.2.l \(\chi_{3750}(557, \cdot)\) n/a 1280 8
3750.2.m \(\chi_{3750}(151, \cdot)\) n/a 1520 20
3750.2.o \(\chi_{3750}(49, \cdot)\) n/a 1480 20
3750.2.r \(\chi_{3750}(107, \cdot)\) n/a 6000 40
3750.2.s \(\chi_{3750}(31, \cdot)\) n/a 12400 100
3750.2.u \(\chi_{3750}(19, \cdot)\) n/a 12600 100
3750.2.x \(\chi_{3750}(17, \cdot)\) n/a 50000 200

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3750))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3750)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(250))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(375))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(625))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(750))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1250))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1875))\)\(^{\oplus 2}\)