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Properties

Label 1536.2
Level 1536
Weight 2
Dimension 27424
Nonzero newspaces 14
Sturm bound 262144
Trace bound 49

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Defining parameters

Level: \( N \) = \( 1536 = 2^{9} \cdot 3 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 14 \)
Sturm bound: \(262144\)
Trace bound: \(49\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1536))\).

Total New Old
Modular forms 67072 27872 39200
Cusp forms 64001 27424 36577
Eisenstein series 3071 448 2623

Trace form

\( 27424 q - 48 q^{3} - 128 q^{4} - 64 q^{6} - 96 q^{7} - 80 q^{9} + O(q^{10}) \) \( 27424 q - 48 q^{3} - 128 q^{4} - 64 q^{6} - 96 q^{7} - 80 q^{9} - 128 q^{10} - 64 q^{12} - 128 q^{13} - 48 q^{15} - 128 q^{16} - 64 q^{18} - 96 q^{19} - 64 q^{21} - 128 q^{22} - 64 q^{24} - 160 q^{25} - 48 q^{27} - 128 q^{28} - 64 q^{30} - 96 q^{31} - 112 q^{33} - 128 q^{34} - 64 q^{36} - 128 q^{37} - 48 q^{39} - 128 q^{40} - 64 q^{42} - 96 q^{43} - 64 q^{45} - 128 q^{46} - 64 q^{48} - 192 q^{49} - 48 q^{51} - 128 q^{52} - 64 q^{54} - 96 q^{55} - 80 q^{57} - 128 q^{58} - 64 q^{60} - 128 q^{61} - 32 q^{63} - 128 q^{64} - 64 q^{66} - 96 q^{67} - 64 q^{69} - 128 q^{70} - 64 q^{72} - 160 q^{73} - 48 q^{75} - 128 q^{76} - 64 q^{78} - 96 q^{79} - 96 q^{81} - 128 q^{82} - 64 q^{84} - 128 q^{85} - 48 q^{87} - 128 q^{88} - 64 q^{90} - 96 q^{91} - 16 q^{93} - 128 q^{94} - 64 q^{96} - 224 q^{97} - 48 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1536))\)

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
1536.2.a \(\chi_{1536}(1, \cdot)\) 1536.2.a.a 2 1
1536.2.a.b 2
1536.2.a.c 2
1536.2.a.d 2
1536.2.a.e 2
1536.2.a.f 2
1536.2.a.g 2
1536.2.a.h 2
1536.2.a.i 2
1536.2.a.j 2
1536.2.a.k 2
1536.2.a.l 2
1536.2.a.m 4
1536.2.a.n 4
1536.2.c \(\chi_{1536}(1535, \cdot)\) 1536.2.c.a 2 1
1536.2.c.b 2
1536.2.c.c 2
1536.2.c.d 2
1536.2.c.e 4
1536.2.c.f 4
1536.2.c.g 4
1536.2.c.h 4
1536.2.c.i 4
1536.2.c.j 4
1536.2.c.k 8
1536.2.c.l 8
1536.2.c.m 16
1536.2.d \(\chi_{1536}(769, \cdot)\) 1536.2.d.a 4 1
1536.2.d.b 4
1536.2.d.c 4
1536.2.d.d 4
1536.2.d.e 4
1536.2.d.f 4
1536.2.d.g 8
1536.2.f \(\chi_{1536}(767, \cdot)\) 1536.2.f.a 4 1
1536.2.f.b 4
1536.2.f.c 4
1536.2.f.d 4
1536.2.f.e 4
1536.2.f.f 4
1536.2.f.g 4
1536.2.f.h 4
1536.2.f.i 4
1536.2.f.j 4
1536.2.f.k 8
1536.2.f.l 16
1536.2.j \(\chi_{1536}(385, \cdot)\) 1536.2.j.a 4 2
1536.2.j.b 4
1536.2.j.c 4
1536.2.j.d 4
1536.2.j.e 8
1536.2.j.f 8
1536.2.j.g 8
1536.2.j.h 8
1536.2.j.i 8
1536.2.j.j 8
1536.2.k \(\chi_{1536}(383, \cdot)\) n/a 128 2
1536.2.n \(\chi_{1536}(193, \cdot)\) n/a 128 4
1536.2.o \(\chi_{1536}(191, \cdot)\) n/a 224 4
1536.2.r \(\chi_{1536}(97, \cdot)\) n/a 256 8
1536.2.s \(\chi_{1536}(95, \cdot)\) n/a 480 8
1536.2.v \(\chi_{1536}(49, \cdot)\) n/a 512 16
1536.2.w \(\chi_{1536}(47, \cdot)\) n/a 992 16
1536.2.z \(\chi_{1536}(25, \cdot)\) None 0 32
1536.2.ba \(\chi_{1536}(23, \cdot)\) None 0 32
1536.2.bd \(\chi_{1536}(13, \cdot)\) n/a 8192 64
1536.2.be \(\chi_{1536}(11, \cdot)\) n/a 16256 64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1536))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1536)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(512))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(768))\)\(^{\oplus 2}\)