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Properties

Label 6625.2
Level 6625
Weight 2
Dimension 1609728
Nonzero newspaces 36
Sturm bound 7020000

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Defining parameters

Level: \( N \) = \( 6625 = 5^{3} \cdot 53 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(7020000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6625))\).

Total New Old
Modular forms 1764360 1622784 141576
Cusp forms 1745641 1609728 135913
Eisenstein series 18719 13056 5663

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6625))\)

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
6625.2.a \(\chi_{6625}(1, \cdot)\) 6625.2.a.a 2 1
6625.2.a.b 2
6625.2.a.c 2
6625.2.a.d 2
6625.2.a.e 48
6625.2.a.f 48
6625.2.a.g 50
6625.2.a.h 50
6625.2.a.i 52
6625.2.a.j 52
6625.2.a.k 54
6625.2.a.l 54
6625.2.b \(\chi_{6625}(3499, \cdot)\) n/a 416 1
6625.2.c \(\chi_{6625}(3126, \cdot)\) n/a 432 1
6625.2.d \(\chi_{6625}(6624, \cdot)\) n/a 432 1
6625.2.e \(\chi_{6625}(818, \cdot)\) n/a 864 2
6625.2.j \(\chi_{6625}(182, \cdot)\) n/a 864 2
6625.2.k \(\chi_{6625}(1326, \cdot)\) n/a 1560 4
6625.2.l \(\chi_{6625}(1324, \cdot)\) n/a 1600 4
6625.2.m \(\chi_{6625}(849, \cdot)\) n/a 1560 4
6625.2.n \(\chi_{6625}(476, \cdot)\) n/a 1592 4
6625.2.o \(\chi_{6625}(501, \cdot)\) n/a 5184 12
6625.2.p \(\chi_{6625}(1143, \cdot)\) n/a 3192 8
6625.2.u \(\chi_{6625}(507, \cdot)\) n/a 3192 8
6625.2.v \(\chi_{6625}(266, \cdot)\) n/a 13000 20
6625.2.w \(\chi_{6625}(249, \cdot)\) n/a 5184 12
6625.2.x \(\chi_{6625}(626, \cdot)\) n/a 5184 12
6625.2.y \(\chi_{6625}(1374, \cdot)\) n/a 5184 12
6625.2.z \(\chi_{6625}(211, \cdot)\) n/a 13480 20
6625.2.ba \(\chi_{6625}(264, \cdot)\) n/a 13440 20
6625.2.bb \(\chi_{6625}(54, \cdot)\) n/a 13000 20
6625.2.bc \(\chi_{6625}(432, \cdot)\) n/a 10368 24
6625.2.bh \(\chi_{6625}(193, \cdot)\) n/a 10368 24
6625.2.bi \(\chi_{6625}(201, \cdot)\) n/a 19200 48
6625.2.bk \(\chi_{6625}(83, \cdot)\) n/a 26920 40
6625.2.bn \(\chi_{6625}(23, \cdot)\) n/a 26920 40
6625.2.bp \(\chi_{6625}(176, \cdot)\) n/a 19104 48
6625.2.bq \(\chi_{6625}(24, \cdot)\) n/a 19104 48
6625.2.br \(\chi_{6625}(149, \cdot)\) n/a 19200 48
6625.2.bs \(\chi_{6625}(18, \cdot)\) n/a 38304 96
6625.2.bx \(\chi_{6625}(157, \cdot)\) n/a 38304 96
6625.2.by \(\chi_{6625}(16, \cdot)\) n/a 161280 240
6625.2.bz \(\chi_{6625}(44, \cdot)\) n/a 161760 240
6625.2.ca \(\chi_{6625}(4, \cdot)\) n/a 161280 240
6625.2.cb \(\chi_{6625}(6, \cdot)\) n/a 161760 240
6625.2.cd \(\chi_{6625}(2, \cdot)\) n/a 323040 480
6625.2.cg \(\chi_{6625}(3, \cdot)\) n/a 323040 480

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6625))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6625)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(265))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1325))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6625))\)\(^{\oplus 1}\)