Properties

Label 3072.2
Level 3072
Weight 2
Dimension 110112
Nonzero newspaces 16
Sturm bound 1048576
Trace bound 233

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Defining parameters

Level: \( N \) = \( 3072 = 2^{10} \cdot 3 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(1048576\)
Trace bound: \(233\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3072))\).

Total New Old
Modular forms 265472 111072 154400
Cusp forms 258817 110112 148705
Eisenstein series 6655 960 5695

Trace form

\( 110112q - 96q^{3} - 256q^{4} - 128q^{6} - 192q^{7} - 160q^{9} + O(q^{10}) \) \( 110112q - 96q^{3} - 256q^{4} - 128q^{6} - 192q^{7} - 160q^{9} - 256q^{10} - 128q^{12} - 256q^{13} - 96q^{15} - 256q^{16} - 128q^{18} - 192q^{19} - 128q^{21} - 256q^{22} - 128q^{24} - 320q^{25} - 96q^{27} - 256q^{28} - 128q^{30} - 192q^{31} - 224q^{33} - 256q^{34} - 128q^{36} - 256q^{37} - 96q^{39} - 256q^{40} - 128q^{42} - 192q^{43} - 128q^{45} - 256q^{46} - 128q^{48} - 384q^{49} - 96q^{51} - 256q^{52} - 128q^{54} - 192q^{55} - 160q^{57} - 256q^{58} - 128q^{60} - 256q^{61} - 96q^{63} - 256q^{64} - 128q^{66} - 192q^{67} - 128q^{69} - 256q^{70} - 128q^{72} - 320q^{73} - 96q^{75} - 256q^{76} - 128q^{78} - 192q^{79} - 192q^{81} - 256q^{82} - 128q^{84} - 256q^{85} - 96q^{87} - 256q^{88} - 128q^{90} - 192q^{91} - 128q^{93} - 256q^{94} - 128q^{96} - 448q^{97} - 96q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3072))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3072.2.a \(\chi_{3072}(1, \cdot)\) 3072.2.a.a 2 1
3072.2.a.b 2
3072.2.a.c 2
3072.2.a.d 2
3072.2.a.e 2
3072.2.a.f 2
3072.2.a.g 2
3072.2.a.h 2
3072.2.a.i 4
3072.2.a.j 4
3072.2.a.k 4
3072.2.a.l 4
3072.2.a.m 4
3072.2.a.n 4
3072.2.a.o 4
3072.2.a.p 4
3072.2.a.q 4
3072.2.a.r 4
3072.2.a.s 4
3072.2.a.t 4
3072.2.c \(\chi_{3072}(3071, \cdot)\) n/a 120 1
3072.2.d \(\chi_{3072}(1537, \cdot)\) 3072.2.d.a 4 1
3072.2.d.b 4
3072.2.d.c 4
3072.2.d.d 4
3072.2.d.e 8
3072.2.d.f 8
3072.2.d.g 8
3072.2.d.h 8
3072.2.d.i 8
3072.2.d.j 8
3072.2.f \(\chi_{3072}(1535, \cdot)\) n/a 120 1
3072.2.j \(\chi_{3072}(769, \cdot)\) n/a 128 2
3072.2.k \(\chi_{3072}(767, \cdot)\) n/a 240 2
3072.2.n \(\chi_{3072}(385, \cdot)\) n/a 256 4
3072.2.o \(\chi_{3072}(383, \cdot)\) n/a 512 4
3072.2.r \(\chi_{3072}(193, \cdot)\) n/a 512 8
3072.2.s \(\chi_{3072}(191, \cdot)\) n/a 960 8
3072.2.v \(\chi_{3072}(97, \cdot)\) n/a 1024 16
3072.2.w \(\chi_{3072}(95, \cdot)\) n/a 1984 16
3072.2.z \(\chi_{3072}(49, \cdot)\) n/a 2048 32
3072.2.ba \(\chi_{3072}(47, \cdot)\) n/a 4032 32
3072.2.bd \(\chi_{3072}(25, \cdot)\) None 0 64
3072.2.be \(\chi_{3072}(23, \cdot)\) None 0 64
3072.2.bh \(\chi_{3072}(13, \cdot)\) n/a 32768 128
3072.2.bi \(\chi_{3072}(11, \cdot)\) n/a 65280 128

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3072))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3072)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(512))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(768))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1024))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1536))\)\(^{\oplus 2}\)