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Properties

Label 3380.1
Level 3380
Weight 1
Dimension 378
Nonzero newspaces 14
Newform subspaces 47
Sturm bound 681408
Trace bound 4

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Defining parameters

Level: \( N \) = \( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 14 \)
Newform subspaces: \( 47 \)
Sturm bound: \(681408\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3380))\).

Total New Old
Modular forms 5074 1604 3470
Cusp forms 514 378 136
Eisenstein series 4560 1226 3334

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 378 0 0 0

Trace form

\( 378 q + 12 q^{8} + 6 q^{10} - 24 q^{14} + 12 q^{17} + 12 q^{18} + 6 q^{20} + 12 q^{29} + 12 q^{37} + 12 q^{41} + 6 q^{45} - 18 q^{50} - 6 q^{52} - 12 q^{58} + 12 q^{61} - 12 q^{64} + 3 q^{65} - 12 q^{68}+ \cdots + 6 q^{85}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3380))\)

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
3380.1.b \(\chi_{3380}(1691, \cdot)\) None 0 1
3380.1.e \(\chi_{3380}(1351, \cdot)\) None 0 1
3380.1.g \(\chi_{3380}(3379, \cdot)\) 3380.1.g.a 2 1
3380.1.g.b 2
3380.1.g.c 6
3380.1.g.d 6
3380.1.h \(\chi_{3380}(339, \cdot)\) 3380.1.h.a 2 1
3380.1.h.b 3
3380.1.h.c 3
3380.1.h.d 3
3380.1.h.e 3
3380.1.h.f 4
3380.1.k \(\chi_{3380}(1789, \cdot)\) None 0 2
3380.1.l \(\chi_{3380}(2127, \cdot)\) 3380.1.l.a 2 2
3380.1.l.b 4
3380.1.l.c 4
3380.1.n \(\chi_{3380}(337, \cdot)\) None 0 2
3380.1.q \(\chi_{3380}(677, \cdot)\) None 0 2
3380.1.s \(\chi_{3380}(2267, \cdot)\) 3380.1.s.a 2 2
3380.1.s.b 4
3380.1.s.c 4
3380.1.t \(\chi_{3380}(3141, \cdot)\) None 0 2
3380.1.v \(\chi_{3380}(2219, \cdot)\) 3380.1.v.a 4 2
3380.1.v.b 4
3380.1.v.c 4
3380.1.v.d 6
3380.1.v.e 6
3380.1.v.f 6
3380.1.v.g 6
3380.1.w \(\chi_{3380}(699, \cdot)\) 3380.1.w.a 2 2
3380.1.w.b 2
3380.1.w.c 2
3380.1.w.d 2
3380.1.w.e 12
3380.1.w.f 12
3380.1.y \(\chi_{3380}(2051, \cdot)\) None 0 2
3380.1.bb \(\chi_{3380}(191, \cdot)\) None 0 2
3380.1.bd \(\chi_{3380}(1441, \cdot)\) None 0 4
3380.1.be \(\chi_{3380}(587, \cdot)\) 3380.1.be.a 4 4
3380.1.be.b 4
3380.1.be.c 4
3380.1.be.d 4
3380.1.be.e 4
3380.1.bh \(\chi_{3380}(653, \cdot)\) None 0 4
3380.1.bi \(\chi_{3380}(1037, \cdot)\) None 0 4
3380.1.bl \(\chi_{3380}(427, \cdot)\) 3380.1.bl.a 4 4
3380.1.bl.b 4
3380.1.bl.c 4
3380.1.bl.d 4
3380.1.bl.e 4
3380.1.bm \(\chi_{3380}(89, \cdot)\) None 0 4
3380.1.bp \(\chi_{3380}(79, \cdot)\) None 0 12
3380.1.bq \(\chi_{3380}(259, \cdot)\) 3380.1.bq.a 12 12
3380.1.bq.b 12
3380.1.bs \(\chi_{3380}(51, \cdot)\) None 0 12
3380.1.bv \(\chi_{3380}(131, \cdot)\) None 0 12
3380.1.by \(\chi_{3380}(21, \cdot)\) None 0 24
3380.1.bz \(\chi_{3380}(187, \cdot)\) 3380.1.bz.a 24 24
3380.1.cb \(\chi_{3380}(53, \cdot)\) None 0 24
3380.1.ce \(\chi_{3380}(77, \cdot)\) None 0 24
3380.1.cg \(\chi_{3380}(47, \cdot)\) 3380.1.cg.a 24 24
3380.1.ch \(\chi_{3380}(109, \cdot)\) None 0 24
3380.1.cj \(\chi_{3380}(211, \cdot)\) None 0 24
3380.1.cm \(\chi_{3380}(231, \cdot)\) None 0 24
3380.1.co \(\chi_{3380}(179, \cdot)\) 3380.1.co.a 24 24
3380.1.co.b 24
3380.1.cp \(\chi_{3380}(139, \cdot)\) None 0 24
3380.1.cr \(\chi_{3380}(149, \cdot)\) None 0 48
3380.1.cs \(\chi_{3380}(7, \cdot)\) 3380.1.cs.a 48 48
3380.1.cv \(\chi_{3380}(17, \cdot)\) None 0 48
3380.1.cw \(\chi_{3380}(113, \cdot)\) None 0 48
3380.1.cz \(\chi_{3380}(63, \cdot)\) 3380.1.cz.a 48 48
3380.1.da \(\chi_{3380}(41, \cdot)\) None 0 48

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3380))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3380)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(260))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(676))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(845))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1690))\)\(^{\oplus 2}\)