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Properties

Label 1932.2
Level 1932
Weight 2
Dimension 41920
Nonzero newspaces 32
Sturm bound 405504
Trace bound 15

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Defining parameters

Level: \( N \) = \( 1932 = 2^{2} \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(405504\)
Trace bound: \(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1932))\).

Total New Old
Modular forms 104016 42768 61248
Cusp forms 98737 41920 56817
Eisenstein series 5279 848 4431

Trace form

\( 41920 q - 2 q^{3} - 76 q^{4} - 12 q^{5} - 32 q^{6} - 16 q^{7} + 12 q^{8} - 66 q^{9} + O(q^{10}) \) \( 41920 q - 2 q^{3} - 76 q^{4} - 12 q^{5} - 32 q^{6} - 16 q^{7} + 12 q^{8} - 66 q^{9} - 40 q^{10} + 12 q^{11} - 8 q^{12} - 108 q^{13} + 48 q^{14} + 14 q^{15} - 28 q^{16} - 20 q^{17} - 8 q^{18} - 12 q^{19} - 73 q^{21} - 200 q^{22} - 76 q^{23} - 100 q^{24} - 180 q^{25} - 60 q^{26} - 62 q^{27} - 194 q^{28} + 28 q^{29} - 104 q^{30} - 36 q^{31} - 60 q^{32} - 116 q^{33} - 48 q^{34} + 32 q^{35} - 126 q^{36} + 28 q^{37} + 184 q^{38} + 12 q^{39} + 216 q^{40} + 40 q^{41} - 41 q^{42} + 96 q^{43} + 260 q^{44} - 122 q^{45} + 240 q^{46} + 140 q^{47} + 24 q^{48} - 124 q^{49} + 224 q^{50} + 46 q^{51} + 304 q^{52} + 40 q^{53} - 96 q^{54} + 176 q^{55} + 74 q^{56} - 46 q^{57} + 132 q^{58} + 112 q^{59} - 24 q^{60} - 96 q^{61} + 89 q^{63} - 136 q^{64} + 12 q^{65} - 74 q^{66} + 120 q^{67} + 72 q^{68} + 34 q^{69} - 76 q^{70} + 16 q^{72} - 60 q^{73} + 88 q^{74} + 178 q^{75} - 140 q^{76} + 176 q^{77} - 90 q^{78} + 112 q^{79} - 252 q^{80} + 118 q^{81} - 184 q^{82} + 112 q^{83} + 19 q^{84} + 248 q^{85} - 308 q^{86} + 108 q^{87} - 200 q^{88} + 240 q^{89} - 266 q^{90} + 48 q^{91} - 312 q^{92} + 342 q^{93} - 348 q^{94} + 168 q^{95} - 330 q^{96} - 156 q^{97} + 62 q^{98} + 196 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1932))\)

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
1932.2.a \(\chi_{1932}(1, \cdot)\) 1932.2.a.a 1 1
1932.2.a.b 1
1932.2.a.c 2
1932.2.a.d 2
1932.2.a.e 2
1932.2.a.f 2
1932.2.a.g 2
1932.2.a.h 2
1932.2.a.i 3
1932.2.a.j 3
1932.2.b \(\chi_{1932}(1931, \cdot)\) n/a 376 1
1932.2.c \(\chi_{1932}(139, \cdot)\) n/a 176 1
1932.2.h \(\chi_{1932}(323, \cdot)\) n/a 264 1
1932.2.i \(\chi_{1932}(1471, \cdot)\) n/a 144 1
1932.2.j \(\chi_{1932}(461, \cdot)\) 1932.2.j.a 4 1
1932.2.j.b 56
1932.2.k \(\chi_{1932}(1609, \cdot)\) 1932.2.k.a 32 1
1932.2.p \(\chi_{1932}(1793, \cdot)\) 1932.2.p.a 48 1
1932.2.q \(\chi_{1932}(277, \cdot)\) 1932.2.q.a 2 2
1932.2.q.b 2
1932.2.q.c 2
1932.2.q.d 2
1932.2.q.e 4
1932.2.q.f 12
1932.2.q.g 16
1932.2.q.h 20
1932.2.t \(\chi_{1932}(137, \cdot)\) n/a 128 2
1932.2.u \(\chi_{1932}(229, \cdot)\) 1932.2.u.a 64 2
1932.2.v \(\chi_{1932}(185, \cdot)\) n/a 116 2
1932.2.ba \(\chi_{1932}(919, \cdot)\) n/a 384 2
1932.2.bb \(\chi_{1932}(599, \cdot)\) n/a 704 2
1932.2.bc \(\chi_{1932}(691, \cdot)\) n/a 352 2
1932.2.bd \(\chi_{1932}(551, \cdot)\) n/a 752 2
1932.2.bg \(\chi_{1932}(85, \cdot)\) n/a 240 10
1932.2.bh \(\chi_{1932}(113, \cdot)\) n/a 480 10
1932.2.bm \(\chi_{1932}(97, \cdot)\) n/a 320 10
1932.2.bn \(\chi_{1932}(41, \cdot)\) n/a 640 10
1932.2.bo \(\chi_{1932}(43, \cdot)\) n/a 1440 10
1932.2.bp \(\chi_{1932}(71, \cdot)\) n/a 2880 10
1932.2.bu \(\chi_{1932}(55, \cdot)\) n/a 1920 10
1932.2.bv \(\chi_{1932}(83, \cdot)\) n/a 3760 10
1932.2.bw \(\chi_{1932}(25, \cdot)\) n/a 640 20
1932.2.bz \(\chi_{1932}(143, \cdot)\) n/a 7520 20
1932.2.ca \(\chi_{1932}(31, \cdot)\) n/a 3840 20
1932.2.cb \(\chi_{1932}(95, \cdot)\) n/a 7520 20
1932.2.cc \(\chi_{1932}(67, \cdot)\) n/a 3840 20
1932.2.ch \(\chi_{1932}(101, \cdot)\) n/a 1280 20
1932.2.ci \(\chi_{1932}(61, \cdot)\) n/a 640 20
1932.2.cj \(\chi_{1932}(53, \cdot)\) n/a 1280 20

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1932))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1932)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(322))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(483))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(644))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(966))\)\(^{\oplus 2}\)