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Properties

Label 3564.1
Level 3564
Weight 1
Dimension 88
Nonzero newspaces 6
Newform subspaces 16
Sturm bound 699840
Trace bound 25

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Defining parameters

Level: \( N \) = \( 3564 = 2^{2} \cdot 3^{4} \cdot 11 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 16 \)
Sturm bound: \(699840\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3564))\).

Total New Old
Modular forms 5740 1096 4644
Cusp forms 340 88 252
Eisenstein series 5400 1008 4392

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 72 0 0 16

Trace form

\( 88 q - 3 q^{5} + 2 q^{7} + O(q^{10}) \) \( 88 q - 3 q^{5} + 2 q^{7} - 4 q^{13} - 8 q^{16} + 4 q^{19} + 4 q^{22} + 3 q^{25} + 5 q^{31} + 4 q^{34} - 10 q^{37} + 6 q^{47} - 2 q^{49} - 10 q^{55} + 4 q^{58} - 3 q^{59} - 4 q^{61} + 11 q^{67} - 8 q^{70} - 8 q^{73} - 18 q^{75} - 8 q^{82} + 2 q^{85} - 4 q^{88} - 15 q^{89} - 12 q^{91} - 18 q^{93} + 19 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3564))\)

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
3564.1.d \(\chi_{3564}(3563, \cdot)\) None 0 1
3564.1.e \(\chi_{3564}(485, \cdot)\) None 0 1
3564.1.f \(\chi_{3564}(1297, \cdot)\) 3564.1.f.a 1 1
3564.1.f.b 1
3564.1.f.c 1
3564.1.f.d 1
3564.1.g \(\chi_{3564}(1783, \cdot)\) None 0 1
3564.1.l \(\chi_{3564}(595, \cdot)\) None 0 2
3564.1.m \(\chi_{3564}(109, \cdot)\) 3564.1.m.a 2 2
3564.1.m.b 2
3564.1.n \(\chi_{3564}(1673, \cdot)\) None 0 2
3564.1.o \(\chi_{3564}(1187, \cdot)\) 3564.1.o.a 2 2
3564.1.o.b 2
3564.1.o.c 2
3564.1.o.d 2
3564.1.o.e 8
3564.1.t \(\chi_{3564}(163, \cdot)\) None 0 4
3564.1.u \(\chi_{3564}(325, \cdot)\) None 0 4
3564.1.v \(\chi_{3564}(1457, \cdot)\) None 0 4
3564.1.w \(\chi_{3564}(1295, \cdot)\) None 0 4
3564.1.ba \(\chi_{3564}(395, \cdot)\) None 0 6
3564.1.bc \(\chi_{3564}(199, \cdot)\) None 0 6
3564.1.be \(\chi_{3564}(89, \cdot)\) None 0 6
3564.1.bg \(\chi_{3564}(505, \cdot)\) 3564.1.bg.a 6 6
3564.1.bg.b 6
3564.1.bk \(\chi_{3564}(107, \cdot)\) None 0 8
3564.1.bl \(\chi_{3564}(53, \cdot)\) 3564.1.bl.a 16 8
3564.1.bm \(\chi_{3564}(217, \cdot)\) None 0 8
3564.1.bn \(\chi_{3564}(379, \cdot)\) None 0 8
3564.1.br \(\chi_{3564}(67, \cdot)\) None 0 18
3564.1.bs \(\chi_{3564}(241, \cdot)\) 3564.1.bs.a 18 18
3564.1.bs.b 18
3564.1.bv \(\chi_{3564}(221, \cdot)\) None 0 18
3564.1.bw \(\chi_{3564}(131, \cdot)\) None 0 18
3564.1.bx \(\chi_{3564}(73, \cdot)\) None 0 24
3564.1.bz \(\chi_{3564}(125, \cdot)\) None 0 24
3564.1.cb \(\chi_{3564}(91, \cdot)\) None 0 24
3564.1.cd \(\chi_{3564}(35, \cdot)\) None 0 24
3564.1.cf \(\chi_{3564}(5, \cdot)\) None 0 72
3564.1.cg \(\chi_{3564}(83, \cdot)\) None 0 72
3564.1.cj \(\chi_{3564}(31, \cdot)\) None 0 72
3564.1.ck \(\chi_{3564}(13, \cdot)\) None 0 72

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3564))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3564)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 15}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(297))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(594))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(891))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1188))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1782))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3564))\)\(^{\oplus 1}\)