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Properties

Label 3136.2
Level 3136
Weight 2
Dimension 161437
Nonzero newspaces 32
Sturm bound 1204224
Trace bound 25

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Defining parameters

Level: \( N \) = \( 3136 = 2^{6} \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(1204224\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3136))\).

Total New Old
Modular forms 305376 163571 141805
Cusp forms 296737 161437 135300
Eisenstein series 8639 2134 6505

Trace form

\( 161437 q - 248 q^{2} - 186 q^{3} - 248 q^{4} - 248 q^{5} - 248 q^{6} - 216 q^{7} - 440 q^{8} - 313 q^{9} + O(q^{10}) \) \( 161437 q - 248 q^{2} - 186 q^{3} - 248 q^{4} - 248 q^{5} - 248 q^{6} - 216 q^{7} - 440 q^{8} - 313 q^{9} - 248 q^{10} - 190 q^{11} - 248 q^{12} - 256 q^{13} - 288 q^{14} - 336 q^{15} - 248 q^{16} - 442 q^{17} - 248 q^{18} - 194 q^{19} - 248 q^{20} - 288 q^{21} - 432 q^{22} - 188 q^{23} - 208 q^{24} - 299 q^{25} - 208 q^{26} - 180 q^{27} - 288 q^{28} - 424 q^{29} - 168 q^{30} - 164 q^{31} - 208 q^{32} - 160 q^{33} - 208 q^{34} - 216 q^{35} - 360 q^{36} - 240 q^{37} - 208 q^{38} - 188 q^{39} - 208 q^{40} - 310 q^{41} - 288 q^{42} - 342 q^{43} - 240 q^{44} - 252 q^{45} - 248 q^{46} - 204 q^{47} - 248 q^{48} - 504 q^{49} - 800 q^{50} - 160 q^{51} - 296 q^{52} - 272 q^{53} - 312 q^{54} - 100 q^{55} - 288 q^{56} - 556 q^{57} - 320 q^{58} - 118 q^{59} - 344 q^{60} - 256 q^{61} - 280 q^{62} - 216 q^{63} - 536 q^{64} - 684 q^{65} - 328 q^{66} - 98 q^{67} - 296 q^{68} - 260 q^{69} - 288 q^{70} - 268 q^{71} - 320 q^{72} - 310 q^{73} - 304 q^{74} - 130 q^{75} - 312 q^{76} - 288 q^{77} - 464 q^{78} - 156 q^{79} - 208 q^{80} - 359 q^{81} - 168 q^{82} - 186 q^{83} - 288 q^{84} - 432 q^{85} - 144 q^{86} - 188 q^{87} - 168 q^{88} - 262 q^{89} - 104 q^{90} - 132 q^{91} - 288 q^{92} - 112 q^{93} - 152 q^{94} - 24 q^{95} - 112 q^{96} + 46 q^{97} - 288 q^{98} - 318 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3136))\)

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
3136.2.a \(\chi_{3136}(1, \cdot)\) 3136.2.a.a 1 1
3136.2.a.b 1
3136.2.a.c 1
3136.2.a.d 1
3136.2.a.e 1
3136.2.a.f 1
3136.2.a.g 1
3136.2.a.h 1
3136.2.a.i 1
3136.2.a.j 1
3136.2.a.k 1
3136.2.a.l 1
3136.2.a.m 1
3136.2.a.n 1
3136.2.a.o 1
3136.2.a.p 1
3136.2.a.q 1
3136.2.a.r 1
3136.2.a.s 1
3136.2.a.t 1
3136.2.a.u 1
3136.2.a.v 1
3136.2.a.w 1
3136.2.a.x 1
3136.2.a.y 1
3136.2.a.z 1
3136.2.a.ba 1
3136.2.a.bb 1
3136.2.a.bc 1
3136.2.a.bd 2
3136.2.a.be 2
3136.2.a.bf 2
3136.2.a.bg 2
3136.2.a.bh 2
3136.2.a.bi 2
3136.2.a.bj 2
3136.2.a.bk 2
3136.2.a.bl 2
3136.2.a.bm 2
3136.2.a.bn 2
3136.2.a.bo 2
3136.2.a.bp 2
3136.2.a.bq 2
3136.2.a.br 2
3136.2.a.bs 2
3136.2.a.bt 2
3136.2.a.bu 2
3136.2.a.bv 2
3136.2.a.bw 2
3136.2.a.bx 2
3136.2.a.by 2
3136.2.a.bz 4
3136.2.b \(\chi_{3136}(1569, \cdot)\) 3136.2.b.a 2 1
3136.2.b.b 2
3136.2.b.c 2
3136.2.b.d 4
3136.2.b.e 4
3136.2.b.f 4
3136.2.b.g 4
3136.2.b.h 4
3136.2.b.i 4
3136.2.b.j 4
3136.2.b.k 8
3136.2.b.l 12
3136.2.b.m 12
3136.2.b.n 16
3136.2.e \(\chi_{3136}(1567, \cdot)\) 3136.2.e.a 8 1
3136.2.e.b 8
3136.2.e.c 8
3136.2.e.d 12
3136.2.e.e 12
3136.2.e.f 32
3136.2.f \(\chi_{3136}(3135, \cdot)\) 3136.2.f.a 2 1
3136.2.f.b 2
3136.2.f.c 4
3136.2.f.d 4
3136.2.f.e 4
3136.2.f.f 4
3136.2.f.g 8
3136.2.f.h 8
3136.2.f.i 8
3136.2.f.j 16
3136.2.f.k 16
3136.2.i \(\chi_{3136}(961, \cdot)\) n/a 152 2
3136.2.j \(\chi_{3136}(783, \cdot)\) n/a 152 2
3136.2.m \(\chi_{3136}(785, \cdot)\) n/a 154 2
3136.2.p \(\chi_{3136}(1599, \cdot)\) n/a 152 2
3136.2.q \(\chi_{3136}(31, \cdot)\) n/a 160 2
3136.2.t \(\chi_{3136}(2529, \cdot)\) n/a 160 2
3136.2.u \(\chi_{3136}(449, \cdot)\) n/a 660 6
3136.2.v \(\chi_{3136}(393, \cdot)\) None 0 4
3136.2.y \(\chi_{3136}(391, \cdot)\) None 0 4
3136.2.ba \(\chi_{3136}(815, \cdot)\) n/a 304 4
3136.2.bb \(\chi_{3136}(177, \cdot)\) n/a 304 4
3136.2.bf \(\chi_{3136}(447, \cdot)\) n/a 660 6
3136.2.bg \(\chi_{3136}(223, \cdot)\) n/a 672 6
3136.2.bj \(\chi_{3136}(225, \cdot)\) n/a 672 6
3136.2.bk \(\chi_{3136}(197, \cdot)\) n/a 2584 8
3136.2.bl \(\chi_{3136}(195, \cdot)\) n/a 2528 8
3136.2.bo \(\chi_{3136}(65, \cdot)\) n/a 1320 12
3136.2.bq \(\chi_{3136}(361, \cdot)\) None 0 8
3136.2.br \(\chi_{3136}(215, \cdot)\) None 0 8
3136.2.bt \(\chi_{3136}(113, \cdot)\) n/a 1320 12
3136.2.bw \(\chi_{3136}(111, \cdot)\) n/a 1320 12
3136.2.bx \(\chi_{3136}(289, \cdot)\) n/a 1344 12
3136.2.ca \(\chi_{3136}(159, \cdot)\) n/a 1344 12
3136.2.cb \(\chi_{3136}(255, \cdot)\) n/a 1320 12
3136.2.cg \(\chi_{3136}(19, \cdot)\) n/a 5056 16
3136.2.ch \(\chi_{3136}(165, \cdot)\) n/a 5056 16
3136.2.ci \(\chi_{3136}(55, \cdot)\) None 0 24
3136.2.cl \(\chi_{3136}(57, \cdot)\) None 0 24
3136.2.cn \(\chi_{3136}(81, \cdot)\) n/a 2640 24
3136.2.co \(\chi_{3136}(47, \cdot)\) n/a 2640 24
3136.2.cq \(\chi_{3136}(27, \cdot)\) n/a 21408 48
3136.2.cr \(\chi_{3136}(29, \cdot)\) n/a 21408 48
3136.2.cv \(\chi_{3136}(87, \cdot)\) None 0 48
3136.2.cw \(\chi_{3136}(9, \cdot)\) None 0 48
3136.2.da \(\chi_{3136}(37, \cdot)\) n/a 42816 96
3136.2.db \(\chi_{3136}(3, \cdot)\) n/a 42816 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3136))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3136)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(448))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(784))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1568))\)\(^{\oplus 2}\)