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Properties

Label 2816.2
Level 2816
Weight 2
Dimension 135000
Nonzero newspaces 24
Sturm bound 983040
Trace bound 129

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Defining parameters

Level: \( N \) = \( 2816 = 2^{8} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(983040\)
Trace bound: \(129\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2816))\).

Total New Old
Modular forms 249280 136872 112408
Cusp forms 242241 135000 107241
Eisenstein series 7039 1872 5167

Trace form

\( 135000 q - 256 q^{2} - 192 q^{3} - 256 q^{4} - 256 q^{5} - 256 q^{6} - 192 q^{7} - 256 q^{8} - 320 q^{9} + O(q^{10}) \) \( 135000 q - 256 q^{2} - 192 q^{3} - 256 q^{4} - 256 q^{5} - 256 q^{6} - 192 q^{7} - 256 q^{8} - 320 q^{9} - 256 q^{10} - 216 q^{11} - 576 q^{12} - 256 q^{13} - 256 q^{14} - 192 q^{15} - 256 q^{16} - 384 q^{17} - 256 q^{18} - 192 q^{19} - 256 q^{20} - 256 q^{21} - 288 q^{22} - 432 q^{23} - 256 q^{24} - 320 q^{25} - 256 q^{26} - 192 q^{27} - 256 q^{28} - 256 q^{29} - 256 q^{30} - 176 q^{31} - 256 q^{32} - 504 q^{33} - 576 q^{34} - 192 q^{35} - 256 q^{36} - 256 q^{37} - 256 q^{38} - 192 q^{39} - 256 q^{40} - 320 q^{41} - 256 q^{42} - 192 q^{43} - 288 q^{44} - 528 q^{45} - 256 q^{46} - 192 q^{47} - 256 q^{48} - 328 q^{49} - 256 q^{50} - 128 q^{51} - 256 q^{52} - 192 q^{53} - 256 q^{54} - 152 q^{55} - 576 q^{56} - 192 q^{57} - 256 q^{58} - 64 q^{59} - 256 q^{60} - 128 q^{61} - 256 q^{62} - 48 q^{63} - 256 q^{64} - 448 q^{65} - 288 q^{66} - 272 q^{67} - 256 q^{68} - 128 q^{69} - 256 q^{70} - 64 q^{71} - 256 q^{72} - 192 q^{73} - 256 q^{74} - 64 q^{75} - 256 q^{76} - 256 q^{77} - 576 q^{78} - 128 q^{79} - 256 q^{80} - 312 q^{81} - 256 q^{82} - 192 q^{83} - 256 q^{84} - 176 q^{85} - 256 q^{86} - 192 q^{87} - 288 q^{88} - 720 q^{89} - 256 q^{90} - 192 q^{91} - 256 q^{92} - 352 q^{93} - 256 q^{94} - 176 q^{95} - 256 q^{96} - 448 q^{97} - 256 q^{98} - 192 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2816))\)

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
2816.2.a \(\chi_{2816}(1, \cdot)\) 2816.2.a.a 2 1
2816.2.a.b 2
2816.2.a.c 2
2816.2.a.d 2
2816.2.a.e 2
2816.2.a.f 2
2816.2.a.g 2
2816.2.a.h 2
2816.2.a.i 3
2816.2.a.j 3
2816.2.a.k 3
2816.2.a.l 3
2816.2.a.m 4
2816.2.a.n 4
2816.2.a.o 5
2816.2.a.p 5
2816.2.a.q 5
2816.2.a.r 5
2816.2.a.s 6
2816.2.a.t 6
2816.2.a.u 6
2816.2.a.v 6
2816.2.c \(\chi_{2816}(1409, \cdot)\) 2816.2.c.a 2 1
2816.2.c.b 2
2816.2.c.c 2
2816.2.c.d 2
2816.2.c.e 2
2816.2.c.f 2
2816.2.c.g 2
2816.2.c.h 2
2816.2.c.i 2
2816.2.c.j 2
2816.2.c.k 2
2816.2.c.l 2
2816.2.c.m 2
2816.2.c.n 2
2816.2.c.o 4
2816.2.c.p 4
2816.2.c.q 4
2816.2.c.r 4
2816.2.c.s 4
2816.2.c.t 4
2816.2.c.u 4
2816.2.c.v 4
2816.2.c.w 4
2816.2.c.x 4
2816.2.c.y 6
2816.2.c.z 6
2816.2.e \(\chi_{2816}(2815, \cdot)\) 2816.2.e.a 2 1
2816.2.e.b 2
2816.2.e.c 4
2816.2.e.d 4
2816.2.e.e 4
2816.2.e.f 4
2816.2.e.g 6
2816.2.e.h 6
2816.2.e.i 6
2816.2.e.j 6
2816.2.e.k 8
2816.2.e.l 8
2816.2.e.m 8
2816.2.e.n 8
2816.2.e.o 16
2816.2.g \(\chi_{2816}(1407, \cdot)\) 2816.2.g.a 4 1
2816.2.g.b 8
2816.2.g.c 8
2816.2.g.d 12
2816.2.g.e 12
2816.2.g.f 12
2816.2.g.g 12
2816.2.g.h 12
2816.2.g.i 12
2816.2.i \(\chi_{2816}(703, \cdot)\) n/a 192 2
2816.2.j \(\chi_{2816}(705, \cdot)\) n/a 160 2
2816.2.m \(\chi_{2816}(257, \cdot)\) n/a 368 4
2816.2.n \(\chi_{2816}(353, \cdot)\) n/a 320 4
2816.2.q \(\chi_{2816}(351, \cdot)\) n/a 368 4
2816.2.s \(\chi_{2816}(127, \cdot)\) n/a 368 4
2816.2.u \(\chi_{2816}(255, \cdot)\) n/a 368 4
2816.2.w \(\chi_{2816}(641, \cdot)\) n/a 368 4
2816.2.z \(\chi_{2816}(177, \cdot)\) n/a 640 8
2816.2.bb \(\chi_{2816}(175, \cdot)\) n/a 752 8
2816.2.be \(\chi_{2816}(449, \cdot)\) n/a 768 8
2816.2.bf \(\chi_{2816}(63, \cdot)\) n/a 768 8
2816.2.bg \(\chi_{2816}(89, \cdot)\) None 0 16
2816.2.bh \(\chi_{2816}(87, \cdot)\) None 0 16
2816.2.bk \(\chi_{2816}(95, \cdot)\) n/a 1472 16
2816.2.bn \(\chi_{2816}(97, \cdot)\) n/a 1472 16
2816.2.bo \(\chi_{2816}(45, \cdot)\) n/a 10240 32
2816.2.bp \(\chi_{2816}(43, \cdot)\) n/a 12224 32
2816.2.bs \(\chi_{2816}(79, \cdot)\) n/a 3008 32
2816.2.bu \(\chi_{2816}(49, \cdot)\) n/a 3008 32
2816.2.by \(\chi_{2816}(9, \cdot)\) None 0 64
2816.2.bz \(\chi_{2816}(7, \cdot)\) None 0 64
2816.2.cc \(\chi_{2816}(19, \cdot)\) n/a 48896 128
2816.2.cd \(\chi_{2816}(5, \cdot)\) n/a 48896 128

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2816))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2816)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(352))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(704))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1408))\)\(^{\oplus 2}\)