Properties

Label 1400.1
Level 1400
Weight 1
Dimension 79
Nonzero newspaces 9
Newform subspaces 18
Sturm bound 115200
Trace bound 9

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Defining parameters

Level: \( N \) = \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 18 \)
Sturm bound: \(115200\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1400))\).

Total New Old
Modular forms 2230 489 1741
Cusp forms 214 79 135
Eisenstein series 2016 410 1606

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 79 0 0 0

Trace form

\( 79q + q^{2} + 5q^{4} + q^{7} + q^{8} + 7q^{9} + O(q^{10}) \) \( 79q + q^{2} + 5q^{4} + q^{7} + q^{8} + 7q^{9} - 2q^{11} - 11q^{14} - 7q^{16} - 9q^{18} - 2q^{19} - 10q^{23} + 14q^{26} + q^{28} + 12q^{31} + q^{32} - 15q^{36} + 16q^{39} - 4q^{41} - 2q^{44} + 4q^{46} - q^{49} - 13q^{56} - 8q^{57} + 4q^{59} - 8q^{60} + 31q^{63} - q^{64} - 8q^{65} + 10q^{71} - 9q^{72} - 2q^{74} - 4q^{76} - 8q^{78} + 2q^{79} - 15q^{81} - 24q^{86} + 4q^{89} - 4q^{91} - 10q^{92} - 2q^{94} + q^{98} + 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1400))\)

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
1400.1.c \(\chi_{1400}(349, \cdot)\) 1400.1.c.a 2 1
1400.1.c.b 4
1400.1.d \(\chi_{1400}(351, \cdot)\) None 0 1
1400.1.f \(\chi_{1400}(601, \cdot)\) None 0 1
1400.1.i \(\chi_{1400}(99, \cdot)\) None 0 1
1400.1.j \(\chi_{1400}(799, \cdot)\) None 0 1
1400.1.m \(\chi_{1400}(1301, \cdot)\) 1400.1.m.a 1 1
1400.1.m.b 2
1400.1.m.c 2
1400.1.m.d 2
1400.1.m.e 2
1400.1.o \(\chi_{1400}(1051, \cdot)\) None 0 1
1400.1.p \(\chi_{1400}(1049, \cdot)\) None 0 1
1400.1.r \(\chi_{1400}(1007, \cdot)\) None 0 2
1400.1.u \(\chi_{1400}(757, \cdot)\) None 0 2
1400.1.v \(\chi_{1400}(57, \cdot)\) None 0 2
1400.1.y \(\chi_{1400}(307, \cdot)\) 1400.1.y.a 4 2
1400.1.y.b 8
1400.1.ba \(\chi_{1400}(51, \cdot)\) 1400.1.ba.a 4 2
1400.1.bc \(\chi_{1400}(649, \cdot)\) None 0 2
1400.1.be \(\chi_{1400}(599, \cdot)\) None 0 2
1400.1.bf \(\chi_{1400}(101, \cdot)\) 1400.1.bf.a 2 2
1400.1.bf.b 2
1400.1.bi \(\chi_{1400}(201, \cdot)\) None 0 2
1400.1.bj \(\chi_{1400}(499, \cdot)\) None 0 2
1400.1.bl \(\chi_{1400}(549, \cdot)\) 1400.1.bl.a 4 2
1400.1.bo \(\chi_{1400}(151, \cdot)\) None 0 2
1400.1.bp \(\chi_{1400}(209, \cdot)\) None 0 4
1400.1.bq \(\chi_{1400}(211, \cdot)\) None 0 4
1400.1.bs \(\chi_{1400}(181, \cdot)\) 1400.1.bs.a 4 4
1400.1.bs.b 4
1400.1.bs.c 8
1400.1.bv \(\chi_{1400}(239, \cdot)\) None 0 4
1400.1.bw \(\chi_{1400}(379, \cdot)\) None 0 4
1400.1.bz \(\chi_{1400}(41, \cdot)\) None 0 4
1400.1.cb \(\chi_{1400}(71, \cdot)\) None 0 4
1400.1.cc \(\chi_{1400}(69, \cdot)\) 1400.1.cc.a 16 4
1400.1.cf \(\chi_{1400}(243, \cdot)\) 1400.1.cf.a 8 4
1400.1.cg \(\chi_{1400}(193, \cdot)\) None 0 4
1400.1.cj \(\chi_{1400}(93, \cdot)\) None 0 4
1400.1.ck \(\chi_{1400}(143, \cdot)\) None 0 4
1400.1.cn \(\chi_{1400}(27, \cdot)\) None 0 8
1400.1.cq \(\chi_{1400}(113, \cdot)\) None 0 8
1400.1.cr \(\chi_{1400}(197, \cdot)\) None 0 8
1400.1.cu \(\chi_{1400}(167, \cdot)\) None 0 8
1400.1.cv \(\chi_{1400}(191, \cdot)\) None 0 8
1400.1.cy \(\chi_{1400}(229, \cdot)\) None 0 8
1400.1.da \(\chi_{1400}(179, \cdot)\) None 0 8
1400.1.db \(\chi_{1400}(241, \cdot)\) None 0 8
1400.1.de \(\chi_{1400}(61, \cdot)\) None 0 8
1400.1.df \(\chi_{1400}(39, \cdot)\) None 0 8
1400.1.dh \(\chi_{1400}(89, \cdot)\) None 0 8
1400.1.dj \(\chi_{1400}(11, \cdot)\) None 0 8
1400.1.dl \(\chi_{1400}(47, \cdot)\) None 0 16
1400.1.dm \(\chi_{1400}(37, \cdot)\) None 0 16
1400.1.dp \(\chi_{1400}(137, \cdot)\) None 0 16
1400.1.dq \(\chi_{1400}(3, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1400))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1400)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(700))\)\(^{\oplus 2}\)