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Properties

Label 1408.2
Level 1408
Weight 2
Dimension 33552
Nonzero newspaces 20
Sturm bound 245760
Trace bound 25

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Defining parameters

Level: \( N \) = \( 1408 = 2^{7} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(245760\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1408))\).

Total New Old
Modular forms 63040 34416 28624
Cusp forms 59841 33552 26289
Eisenstein series 3199 864 2335

Trace form

\( 33552 q - 128 q^{2} - 96 q^{3} - 128 q^{4} - 128 q^{5} - 128 q^{6} - 96 q^{7} - 128 q^{8} - 160 q^{9} + O(q^{10}) \) \( 33552 q - 128 q^{2} - 96 q^{3} - 128 q^{4} - 128 q^{5} - 128 q^{6} - 96 q^{7} - 128 q^{8} - 160 q^{9} - 128 q^{10} - 108 q^{11} - 288 q^{12} - 128 q^{13} - 128 q^{14} - 88 q^{15} - 128 q^{16} - 192 q^{17} - 128 q^{18} - 96 q^{19} - 128 q^{20} - 104 q^{21} - 144 q^{22} - 200 q^{23} - 128 q^{24} - 128 q^{25} - 128 q^{26} - 48 q^{27} - 128 q^{28} - 96 q^{29} - 128 q^{30} - 56 q^{31} - 128 q^{32} - 256 q^{33} - 288 q^{34} - 48 q^{35} - 128 q^{36} - 96 q^{37} - 128 q^{38} - 48 q^{39} - 128 q^{40} - 128 q^{41} - 128 q^{42} - 80 q^{43} - 144 q^{44} - 296 q^{45} - 128 q^{46} - 88 q^{47} - 128 q^{48} - 248 q^{49} - 224 q^{50} - 104 q^{51} - 320 q^{52} - 192 q^{53} - 384 q^{54} - 140 q^{55} - 512 q^{56} - 288 q^{57} - 416 q^{58} - 160 q^{59} - 512 q^{60} - 256 q^{61} - 320 q^{62} - 216 q^{63} - 512 q^{64} - 256 q^{65} - 336 q^{66} - 296 q^{67} - 320 q^{68} - 232 q^{69} - 512 q^{70} - 160 q^{71} - 416 q^{72} - 288 q^{73} - 352 q^{74} - 120 q^{75} - 384 q^{76} - 148 q^{77} - 480 q^{78} - 88 q^{79} - 224 q^{80} - 200 q^{81} - 128 q^{82} - 16 q^{83} - 128 q^{84} - 144 q^{85} - 128 q^{86} + 16 q^{87} - 144 q^{88} - 232 q^{89} - 128 q^{90} - 128 q^{92} - 32 q^{93} - 128 q^{94} + 24 q^{95} - 128 q^{96} - 128 q^{97} - 128 q^{98} - 56 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1408))\)

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
1408.2.a \(\chi_{1408}(1, \cdot)\) 1408.2.a.a 1 1
1408.2.a.b 1
1408.2.a.c 1
1408.2.a.d 1
1408.2.a.e 2
1408.2.a.f 2
1408.2.a.g 2
1408.2.a.h 2
1408.2.a.i 2
1408.2.a.j 2
1408.2.a.k 2
1408.2.a.l 2
1408.2.a.m 2
1408.2.a.n 2
1408.2.a.o 2
1408.2.a.p 2
1408.2.a.q 3
1408.2.a.r 3
1408.2.a.s 3
1408.2.a.t 3
1408.2.c \(\chi_{1408}(705, \cdot)\) 1408.2.c.a 4 1
1408.2.c.b 4
1408.2.c.c 6
1408.2.c.d 6
1408.2.c.e 8
1408.2.c.f 12
1408.2.e \(\chi_{1408}(1407, \cdot)\) 1408.2.e.a 12 1
1408.2.e.b 12
1408.2.e.c 12
1408.2.e.d 12
1408.2.g \(\chi_{1408}(703, \cdot)\) 1408.2.g.a 4 1
1408.2.g.b 4
1408.2.g.c 4
1408.2.g.d 4
1408.2.g.e 8
1408.2.g.f 12
1408.2.g.g 12
1408.2.i \(\chi_{1408}(351, \cdot)\) 1408.2.i.a 44 2
1408.2.i.b 44
1408.2.j \(\chi_{1408}(353, \cdot)\) 1408.2.j.a 40 2
1408.2.j.b 40
1408.2.m \(\chi_{1408}(257, \cdot)\) n/a 192 4
1408.2.n \(\chi_{1408}(177, \cdot)\) n/a 160 4
1408.2.q \(\chi_{1408}(175, \cdot)\) n/a 184 4
1408.2.s \(\chi_{1408}(63, \cdot)\) n/a 192 4
1408.2.u \(\chi_{1408}(127, \cdot)\) n/a 192 4
1408.2.w \(\chi_{1408}(449, \cdot)\) n/a 192 4
1408.2.z \(\chi_{1408}(89, \cdot)\) None 0 8
1408.2.bb \(\chi_{1408}(87, \cdot)\) None 0 8
1408.2.be \(\chi_{1408}(97, \cdot)\) n/a 352 8
1408.2.bf \(\chi_{1408}(95, \cdot)\) n/a 352 8
1408.2.bg \(\chi_{1408}(45, \cdot)\) n/a 2560 16
1408.2.bh \(\chi_{1408}(43, \cdot)\) n/a 3040 16
1408.2.bk \(\chi_{1408}(79, \cdot)\) n/a 736 16
1408.2.bn \(\chi_{1408}(49, \cdot)\) n/a 736 16
1408.2.bo \(\chi_{1408}(7, \cdot)\) None 0 32
1408.2.bq \(\chi_{1408}(9, \cdot)\) None 0 32
1408.2.bu \(\chi_{1408}(5, \cdot)\) n/a 12160 64
1408.2.bv \(\chi_{1408}(19, \cdot)\) n/a 12160 64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1408))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1408)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(352))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(704))\)\(^{\oplus 2}\)