Properties

Label 192.4
Level 192
Weight 4
Dimension 1274
Nonzero newspaces 8
Newform subspaces 27
Sturm bound 8192
Trace bound 11

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Defining parameters

Level: \( N \) = \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 27 \)
Sturm bound: \(8192\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(192))\).

Total New Old
Modular forms 3216 1318 1898
Cusp forms 2928 1274 1654
Eisenstein series 288 44 244

Trace form

\( 1274 q - 6 q^{3} - 16 q^{4} - 8 q^{6} - 8 q^{7} - 10 q^{9} - 16 q^{10} + 40 q^{11} - 8 q^{12} - 160 q^{13} - 128 q^{15} - 16 q^{16} - 208 q^{17} - 8 q^{18} - 60 q^{19} + 4 q^{21} - 960 q^{22} - 1008 q^{24}+ \cdots - 844 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(192))\)

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
192.4.a \(\chi_{192}(1, \cdot)\) 192.4.a.a 1 1
192.4.a.b 1
192.4.a.c 1
192.4.a.d 1
192.4.a.e 1
192.4.a.f 1
192.4.a.g 1
192.4.a.h 1
192.4.a.i 1
192.4.a.j 1
192.4.a.k 1
192.4.a.l 1
192.4.c \(\chi_{192}(191, \cdot)\) 192.4.c.a 2 1
192.4.c.b 4
192.4.c.c 4
192.4.c.d 12
192.4.d \(\chi_{192}(97, \cdot)\) 192.4.d.a 4 1
192.4.d.b 4
192.4.d.c 4
192.4.f \(\chi_{192}(95, \cdot)\) 192.4.f.a 4 1
192.4.f.b 4
192.4.f.c 8
192.4.f.d 8
192.4.j \(\chi_{192}(49, \cdot)\) 192.4.j.a 24 2
192.4.k \(\chi_{192}(47, \cdot)\) 192.4.k.a 44 2
192.4.n \(\chi_{192}(25, \cdot)\) None 0 4
192.4.o \(\chi_{192}(23, \cdot)\) None 0 4
192.4.r \(\chi_{192}(13, \cdot)\) 192.4.r.a 384 8
192.4.s \(\chi_{192}(11, \cdot)\) 192.4.s.a 752 8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(192))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(192)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 2}\)