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Properties

Label 3364.1
Level 3364
Weight 1
Dimension 300
Nonzero newspaces 6
Newform subspaces 17
Sturm bound 706440
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3364 = 2^{2} \cdot 29^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 17 \)
Sturm bound: \(706440\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3364))\).

Total New Old
Modular forms 3326 1449 1877
Cusp forms 316 300 16
Eisenstein series 3010 1149 1861

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 300 0 0 0

Trace form

\( 300 q + q^{2} - q^{4} + 4 q^{5} + 2 q^{6} + q^{8} + q^{9} + O(q^{10}) \) \( 300 q + q^{2} - q^{4} + 4 q^{5} + 2 q^{6} + q^{8} + q^{9} + 2 q^{10} + 4 q^{13} - q^{16} + 2 q^{17} + q^{18} - 10 q^{20} + 2 q^{22} + 2 q^{24} + 3 q^{25} - 12 q^{26} + 26 q^{30} + q^{32} - 2 q^{33} - 12 q^{34} + q^{36} + 2 q^{37} - 4 q^{38} - 12 q^{40} + 2 q^{41} - 12 q^{45} - q^{49} + 3 q^{50} + 4 q^{52} - 10 q^{53} - 2 q^{54} + 4 q^{57} + 2 q^{61} + 2 q^{62} - q^{64} - 12 q^{65} + 2 q^{68} + q^{72} - 12 q^{73} + 2 q^{74} - 2 q^{78} + 4 q^{80} + 3 q^{81} + 2 q^{82} + 4 q^{85} + 2 q^{86} - 26 q^{88} + 2 q^{89} + 2 q^{90} - 2 q^{93} + 2 q^{94} + 2 q^{96} - 12 q^{97} + q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3364))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3364.1.b \(\chi_{3364}(1683, \cdot)\) 3364.1.b.a 2 1
3364.1.b.b 3
3364.1.b.c 3
3364.1.d \(\chi_{3364}(3363, \cdot)\) 3364.1.d.a 6 1
3364.1.f \(\chi_{3364}(41, \cdot)\) None 0 2
3364.1.h \(\chi_{3364}(63, \cdot)\) 3364.1.h.a 6 6
3364.1.h.b 6
3364.1.h.c 12
3364.1.h.d 12
3364.1.h.e 12
3364.1.j \(\chi_{3364}(571, \cdot)\) 3364.1.j.a 6 6
3364.1.j.b 6
3364.1.j.c 6
3364.1.j.d 6
3364.1.j.e 6
3364.1.j.f 12
3364.1.k \(\chi_{3364}(137, \cdot)\) None 0 12
3364.1.n \(\chi_{3364}(115, \cdot)\) None 0 28
3364.1.p \(\chi_{3364}(59, \cdot)\) 3364.1.p.a 28 28
3364.1.q \(\chi_{3364}(17, \cdot)\) None 0 56
3364.1.t \(\chi_{3364}(7, \cdot)\) 3364.1.t.a 168 168
3364.1.v \(\chi_{3364}(35, \cdot)\) None 0 168
3364.1.x \(\chi_{3364}(21, \cdot)\) None 0 336

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3364))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3364)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(841))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1682))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3364))\)\(^{\oplus 1}\)