Properties

Label 1224.2
Level 1224
Weight 2
Dimension 18070
Nonzero newspaces 30
Sturm bound 165888
Trace bound 10

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Defining parameters

Level: \( N \) = \( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(165888\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1224))\).

Total New Old
Modular forms 43008 18610 24398
Cusp forms 39937 18070 21867
Eisenstein series 3071 540 2531

Trace form

\( 18070 q - 44 q^{2} - 58 q^{3} - 44 q^{4} - 8 q^{5} - 48 q^{6} - 44 q^{7} - 20 q^{8} - 110 q^{9} - 96 q^{10} - 14 q^{11} - 36 q^{12} + 4 q^{13} - 20 q^{14} - 16 q^{15} - 28 q^{16} - 76 q^{17} - 128 q^{18}+ \cdots + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1224))\)

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
1224.2.a \(\chi_{1224}(1, \cdot)\) 1224.2.a.a 1 1
1224.2.a.b 1
1224.2.a.c 1
1224.2.a.d 1
1224.2.a.e 1
1224.2.a.f 1
1224.2.a.g 1
1224.2.a.h 1
1224.2.a.i 2
1224.2.a.j 2
1224.2.a.k 2
1224.2.a.l 3
1224.2.a.m 3
1224.2.c \(\chi_{1224}(577, \cdot)\) 1224.2.c.a 2 1
1224.2.c.b 2
1224.2.c.c 2
1224.2.c.d 2
1224.2.c.e 2
1224.2.c.f 2
1224.2.c.g 4
1224.2.c.h 6
1224.2.e \(\chi_{1224}(647, \cdot)\) None 0 1
1224.2.f \(\chi_{1224}(613, \cdot)\) 1224.2.f.a 2 1
1224.2.f.b 4
1224.2.f.c 8
1224.2.f.d 8
1224.2.f.e 12
1224.2.f.f 14
1224.2.f.g 16
1224.2.f.h 16
1224.2.h \(\chi_{1224}(611, \cdot)\) 1224.2.h.a 8 1
1224.2.h.b 8
1224.2.h.c 56
1224.2.j \(\chi_{1224}(35, \cdot)\) 1224.2.j.a 64 1
1224.2.l \(\chi_{1224}(1189, \cdot)\) 1224.2.l.a 4 1
1224.2.l.b 16
1224.2.l.c 18
1224.2.l.d 18
1224.2.l.e 32
1224.2.o \(\chi_{1224}(1223, \cdot)\) None 0 1
1224.2.q \(\chi_{1224}(409, \cdot)\) 1224.2.q.a 2 2
1224.2.q.b 2
1224.2.q.c 2
1224.2.q.d 2
1224.2.q.e 2
1224.2.q.f 8
1224.2.q.g 16
1224.2.q.h 18
1224.2.q.i 20
1224.2.q.j 24
1224.2.r \(\chi_{1224}(251, \cdot)\) n/a 144 2
1224.2.t \(\chi_{1224}(829, \cdot)\) n/a 176 2
1224.2.w \(\chi_{1224}(217, \cdot)\) 1224.2.w.a 2 2
1224.2.w.b 2
1224.2.w.c 2
1224.2.w.d 2
1224.2.w.e 2
1224.2.w.f 2
1224.2.w.g 4
1224.2.w.h 4
1224.2.w.i 6
1224.2.w.j 6
1224.2.w.k 12
1224.2.y \(\chi_{1224}(863, \cdot)\) None 0 2
1224.2.ba \(\chi_{1224}(407, \cdot)\) None 0 2
1224.2.bd \(\chi_{1224}(373, \cdot)\) n/a 424 2
1224.2.bf \(\chi_{1224}(443, \cdot)\) n/a 384 2
1224.2.bh \(\chi_{1224}(203, \cdot)\) n/a 424 2
1224.2.bj \(\chi_{1224}(205, \cdot)\) n/a 384 2
1224.2.bk \(\chi_{1224}(239, \cdot)\) None 0 2
1224.2.bm \(\chi_{1224}(169, \cdot)\) n/a 108 2
1224.2.bq \(\chi_{1224}(145, \cdot)\) 1224.2.bq.a 4 4
1224.2.bq.b 4
1224.2.bq.c 12
1224.2.bq.d 16
1224.2.bq.e 16
1224.2.bq.f 20
1224.2.bq.g 20
1224.2.br \(\chi_{1224}(287, \cdot)\) None 0 4
1224.2.bs \(\chi_{1224}(253, \cdot)\) n/a 352 4
1224.2.bt \(\chi_{1224}(179, \cdot)\) n/a 288 4
1224.2.bx \(\chi_{1224}(625, \cdot)\) n/a 216 4
1224.2.bz \(\chi_{1224}(47, \cdot)\) None 0 4
1224.2.ca \(\chi_{1224}(659, \cdot)\) n/a 848 4
1224.2.cc \(\chi_{1224}(13, \cdot)\) n/a 848 4
1224.2.cf \(\chi_{1224}(233, \cdot)\) n/a 144 8
1224.2.cg \(\chi_{1224}(199, \cdot)\) None 0 8
1224.2.cj \(\chi_{1224}(91, \cdot)\) n/a 704 8
1224.2.ck \(\chi_{1224}(125, \cdot)\) n/a 576 8
1224.2.cm \(\chi_{1224}(229, \cdot)\) n/a 1696 8
1224.2.cn \(\chi_{1224}(59, \cdot)\) n/a 1696 8
1224.2.cs \(\chi_{1224}(25, \cdot)\) n/a 432 8
1224.2.ct \(\chi_{1224}(263, \cdot)\) None 0 8
1224.2.cv \(\chi_{1224}(7, \cdot)\) None 0 16
1224.2.cw \(\chi_{1224}(41, \cdot)\) n/a 864 16
1224.2.cz \(\chi_{1224}(5, \cdot)\) n/a 3392 16
1224.2.da \(\chi_{1224}(139, \cdot)\) n/a 3392 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1224))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1224)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(306))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(408))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(612))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1224))\)\(^{\oplus 1}\)