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Properties

Label 9904.2
Level 9904
Weight 2
Dimension 1721435
Nonzero newspaces 16
Sturm bound 12261120

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Defining parameters

Level: \( N \) = \( 9904 = 2^{4} \cdot 619 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(12261120\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9904))\).

Total New Old
Modular forms 3073932 1726987 1346945
Cusp forms 3056629 1721435 1335194
Eisenstein series 17303 5552 11751

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9904))\)

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
9904.2.a \(\chi_{9904}(1, \cdot)\) 9904.2.a.a 1 1
9904.2.a.b 1
9904.2.a.c 1
9904.2.a.d 2
9904.2.a.e 2
9904.2.a.f 3
9904.2.a.g 8
9904.2.a.h 17
9904.2.a.i 19
9904.2.a.j 21
9904.2.a.k 23
9904.2.a.l 28
9904.2.a.m 29
9904.2.a.n 30
9904.2.a.o 36
9904.2.a.p 40
9904.2.a.q 48
9904.2.b \(\chi_{9904}(4951, \cdot)\) None 0 1
9904.2.c \(\chi_{9904}(4953, \cdot)\) None 0 1
9904.2.h \(\chi_{9904}(9903, \cdot)\) n/a 310 1
9904.2.i \(\chi_{9904}(5937, \cdot)\) n/a 618 2
9904.2.k \(\chi_{9904}(2477, \cdot)\) n/a 2472 2
9904.2.m \(\chi_{9904}(2475, \cdot)\) n/a 2476 2
9904.2.p \(\chi_{9904}(985, \cdot)\) None 0 2
9904.2.q \(\chi_{9904}(5319, \cdot)\) None 0 2
9904.2.r \(\chi_{9904}(367, \cdot)\) n/a 620 2
9904.2.u \(\chi_{9904}(1491, \cdot)\) n/a 4952 4
9904.2.w \(\chi_{9904}(2109, \cdot)\) n/a 4952 4
9904.2.y \(\chi_{9904}(81, \cdot)\) n/a 31518 102
9904.2.z \(\chi_{9904}(47, \cdot)\) n/a 31620 102
9904.2.be \(\chi_{9904}(9, \cdot)\) None 0 102
9904.2.bf \(\chi_{9904}(375, \cdot)\) None 0 102
9904.2.bg \(\chi_{9904}(33, \cdot)\) n/a 63036 204
9904.2.bh \(\chi_{9904}(3, \cdot)\) n/a 252552 204
9904.2.bj \(\chi_{9904}(125, \cdot)\) n/a 252552 204
9904.2.bn \(\chi_{9904}(15, \cdot)\) n/a 63240 204
9904.2.bo \(\chi_{9904}(55, \cdot)\) None 0 204
9904.2.bp \(\chi_{9904}(25, \cdot)\) None 0 204
9904.2.bt \(\chi_{9904}(5, \cdot)\) n/a 505104 408
9904.2.bv \(\chi_{9904}(11, \cdot)\) n/a 505104 408

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9904))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9904)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(619))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1238))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2476))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4952))\)\(^{\oplus 2}\)