↑

Properties

Label 2304.1
Level 2304
Weight 1
Dimension 63
Nonzero newspaces 9
Newform subspaces 20
Sturm bound 294912
Trace bound 25

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 2304 = 2^{8} \cdot 3^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 20 \)
Sturm bound: \(294912\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2304))\).

Total New Old
Modular forms 3050 531 2519
Cusp forms 234 63 171
Eisenstein series 2816 468 2348

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 39 8 16 0

Trace form

\( 63 q + 8 q^{9} + 18 q^{17} + 5 q^{25} - 12 q^{33} + 14 q^{41} - 9 q^{49} + 8 q^{57} + 4 q^{65} + 6 q^{73} + 8 q^{81} - 2 q^{89} - 10 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2304))\)

We only show spaces with odd 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
2304.1.b \(\chi_{2304}(127, \cdot)\) 2304.1.b.a 2 1
2304.1.e \(\chi_{2304}(1025, \cdot)\) 2304.1.e.a 2 1
2304.1.e.b 2
2304.1.g \(\chi_{2304}(1279, \cdot)\) 2304.1.g.a 1 1
2304.1.g.b 1
2304.1.g.c 1
2304.1.g.d 2
2304.1.h \(\chi_{2304}(2177, \cdot)\) 2304.1.h.a 4 1
2304.1.j \(\chi_{2304}(449, \cdot)\) None 0 2
2304.1.m \(\chi_{2304}(703, \cdot)\) 2304.1.m.a 4 2
2304.1.m.b 4
2304.1.n \(\chi_{2304}(641, \cdot)\) None 0 2
2304.1.o \(\chi_{2304}(511, \cdot)\) 2304.1.o.a 2 2
2304.1.o.b 2
2304.1.o.c 4
2304.1.q \(\chi_{2304}(257, \cdot)\) 2304.1.q.a 2 2
2304.1.q.b 2
2304.1.q.c 4
2304.1.t \(\chi_{2304}(895, \cdot)\) 2304.1.t.a 4 2
2304.1.t.b 4
2304.1.u \(\chi_{2304}(415, \cdot)\) None 0 4
2304.1.x \(\chi_{2304}(161, \cdot)\) None 0 4
2304.1.z \(\chi_{2304}(319, \cdot)\) 2304.1.z.a 8 4
2304.1.z.b 8
2304.1.ba \(\chi_{2304}(65, \cdot)\) None 0 4
2304.1.bc \(\chi_{2304}(17, \cdot)\) None 0 8
2304.1.bf \(\chi_{2304}(271, \cdot)\) None 0 8
2304.1.bh \(\chi_{2304}(31, \cdot)\) None 0 8
2304.1.bi \(\chi_{2304}(353, \cdot)\) None 0 8
2304.1.bk \(\chi_{2304}(55, \cdot)\) None 0 16
2304.1.bn \(\chi_{2304}(89, \cdot)\) None 0 16
2304.1.bo \(\chi_{2304}(79, \cdot)\) None 0 16
2304.1.br \(\chi_{2304}(113, \cdot)\) None 0 16
2304.1.bs \(\chi_{2304}(53, \cdot)\) None 0 32
2304.1.bv \(\chi_{2304}(19, \cdot)\) None 0 32
2304.1.bx \(\chi_{2304}(41, \cdot)\) None 0 32
2304.1.by \(\chi_{2304}(7, \cdot)\) None 0 32
2304.1.cb \(\chi_{2304}(5, \cdot)\) None 0 64
2304.1.cc \(\chi_{2304}(43, \cdot)\) None 0 64

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2304))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2304)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 27}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 21}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 14}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 15}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 7}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(576))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(768))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1152))\)\(^{\oplus 2}\)