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Properties

Label 3332.1
Level 3332
Weight 1
Dimension 289
Nonzero newspaces 10
Newform subspaces 45
Sturm bound 677376
Trace bound 16

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Defining parameters

Level: \( N \) = \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 45 \)
Sturm bound: \(677376\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3332))\).

Total New Old
Modular forms 5168 1743 3425
Cusp forms 368 289 79
Eisenstein series 4800 1454 3346

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 289 0 0 0

Trace form

\( 289 q + q^{2} + 5 q^{4} + 2 q^{5} - 5 q^{8} + 5 q^{9} + O(q^{10}) \) \( 289 q + q^{2} + 5 q^{4} + 2 q^{5} - 5 q^{8} + 5 q^{9} - 2 q^{10} + 2 q^{13} + q^{16} + 5 q^{17} - 15 q^{18} - 2 q^{20} + 3 q^{25} - 18 q^{26} - 2 q^{29} + q^{32} - 16 q^{33} + q^{34} - 31 q^{36} + 2 q^{37} + 2 q^{40} - 2 q^{41} - 2 q^{45} - 33 q^{50} + 2 q^{52} - 18 q^{53} + 2 q^{58} + 2 q^{61} - 13 q^{64} + 8 q^{66} + q^{68} + 8 q^{69} - 19 q^{72} - 2 q^{73} - 2 q^{74} - 12 q^{77} + 2 q^{80} + 73 q^{81} - 2 q^{82} - 12 q^{84} - 2 q^{85} + 2 q^{89} - 2 q^{90} - 16 q^{93} + 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3332))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3332.1.c \(\chi_{3332}(2449, \cdot)\) None 0 1
3332.1.d \(\chi_{3332}(1667, \cdot)\) None 0 1
3332.1.g \(\chi_{3332}(883, \cdot)\) 3332.1.g.a 1 1
3332.1.g.b 1
3332.1.g.c 1
3332.1.g.d 1
3332.1.g.e 1
3332.1.g.f 2
3332.1.g.g 2
3332.1.g.h 2
3332.1.g.i 8
3332.1.h \(\chi_{3332}(1665, \cdot)\) None 0 1
3332.1.j \(\chi_{3332}(293, \cdot)\) None 0 2
3332.1.m \(\chi_{3332}(2843, \cdot)\) 3332.1.m.a 2 2
3332.1.m.b 2
3332.1.m.c 2
3332.1.n \(\chi_{3332}(509, \cdot)\) None 0 2
3332.1.o \(\chi_{3332}(67, \cdot)\) 3332.1.o.a 2 2
3332.1.o.b 2
3332.1.o.c 2
3332.1.o.d 2
3332.1.o.e 4
3332.1.o.f 4
3332.1.o.g 16
3332.1.r \(\chi_{3332}(851, \cdot)\) None 0 2
3332.1.s \(\chi_{3332}(1293, \cdot)\) None 0 2
3332.1.w \(\chi_{3332}(491, \cdot)\) 3332.1.w.a 4 4
3332.1.w.b 4
3332.1.w.c 4
3332.1.w.d 4
3332.1.y \(\chi_{3332}(1273, \cdot)\) None 0 4
3332.1.z \(\chi_{3332}(1109, \cdot)\) None 0 4
3332.1.bc \(\chi_{3332}(667, \cdot)\) 3332.1.bc.a 4 4
3332.1.bc.b 4
3332.1.bc.c 4
3332.1.bc.d 4
3332.1.bd \(\chi_{3332}(237, \cdot)\) None 0 6
3332.1.be \(\chi_{3332}(407, \cdot)\) 3332.1.be.a 6 6
3332.1.be.b 6
3332.1.be.c 12
3332.1.bh \(\chi_{3332}(239, \cdot)\) None 0 6
3332.1.bi \(\chi_{3332}(69, \cdot)\) None 0 6
3332.1.bk \(\chi_{3332}(197, \cdot)\) None 0 8
3332.1.bn \(\chi_{3332}(979, \cdot)\) 3332.1.bn.a 8 8
3332.1.bn.b 8
3332.1.bn.c 8
3332.1.bn.d 8
3332.1.bp \(\chi_{3332}(263, \cdot)\) 3332.1.bp.a 8 8
3332.1.bp.b 8
3332.1.bp.c 8
3332.1.bp.d 8
3332.1.br \(\chi_{3332}(117, \cdot)\) None 0 8
3332.1.bt \(\chi_{3332}(183, \cdot)\) None 0 12
3332.1.bw \(\chi_{3332}(13, \cdot)\) None 0 12
3332.1.by \(\chi_{3332}(341, \cdot)\) None 0 12
3332.1.bz \(\chi_{3332}(375, \cdot)\) None 0 12
3332.1.cc \(\chi_{3332}(135, \cdot)\) 3332.1.cc.a 12 12
3332.1.cc.b 12
3332.1.cc.c 24
3332.1.cd \(\chi_{3332}(33, \cdot)\) None 0 12
3332.1.ce \(\chi_{3332}(31, \cdot)\) 3332.1.ce.a 16 16
3332.1.ce.b 16
3332.1.ce.c 16
3332.1.ce.d 16
3332.1.ch \(\chi_{3332}(165, \cdot)\) None 0 16
3332.1.ci \(\chi_{3332}(321, \cdot)\) None 0 24
3332.1.ck \(\chi_{3332}(15, \cdot)\) None 0 24
3332.1.cm \(\chi_{3332}(123, \cdot)\) None 0 24
3332.1.cp \(\chi_{3332}(89, \cdot)\) None 0 24
3332.1.cr \(\chi_{3332}(27, \cdot)\) None 0 48
3332.1.cs \(\chi_{3332}(29, \cdot)\) None 0 48
3332.1.cv \(\chi_{3332}(145, \cdot)\) None 0 48
3332.1.cx \(\chi_{3332}(151, \cdot)\) None 0 48
3332.1.cz \(\chi_{3332}(37, \cdot)\) None 0 96
3332.1.da \(\chi_{3332}(3, \cdot)\) None 0 96

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3332))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3332)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(476))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(833))\)\(^{\oplus 3}\)