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Properties

Label 2656.2
Level 2656
Weight 2
Dimension 123138
Nonzero newspaces 12
Sturm bound 881664
Trace bound 9

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Defining parameters

Level: \( N \) = \( 2656 = 2^{5} \cdot 83 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(881664\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2656))\).

Total New Old
Modular forms 223040 124758 98282
Cusp forms 217793 123138 94655
Eisenstein series 5247 1620 3627

Trace form

\( 123138 q - 320 q^{2} - 238 q^{3} - 320 q^{4} - 316 q^{5} - 320 q^{6} - 238 q^{7} - 320 q^{8} - 478 q^{9} + O(q^{10}) \) \( 123138 q - 320 q^{2} - 238 q^{3} - 320 q^{4} - 316 q^{5} - 320 q^{6} - 238 q^{7} - 320 q^{8} - 478 q^{9} - 336 q^{10} - 238 q^{11} - 352 q^{12} - 332 q^{13} - 352 q^{14} - 246 q^{15} - 360 q^{16} - 168 q^{17} - 360 q^{18} - 238 q^{19} - 352 q^{20} - 320 q^{21} - 344 q^{22} - 254 q^{23} - 296 q^{24} - 482 q^{25} - 280 q^{26} - 286 q^{27} - 280 q^{28} - 300 q^{29} - 256 q^{30} - 278 q^{31} - 280 q^{32} - 804 q^{33} - 296 q^{34} - 286 q^{35} - 264 q^{36} - 316 q^{37} - 336 q^{38} - 286 q^{39} - 344 q^{40} - 504 q^{41} - 360 q^{42} - 254 q^{43} - 400 q^{44} - 356 q^{45} - 384 q^{46} - 246 q^{47} - 424 q^{48} - 150 q^{49} - 400 q^{50} - 230 q^{51} - 336 q^{52} - 380 q^{53} - 344 q^{54} - 174 q^{55} - 344 q^{56} - 484 q^{57} - 312 q^{58} - 174 q^{59} - 312 q^{60} - 364 q^{61} - 280 q^{62} - 150 q^{63} - 248 q^{64} - 780 q^{65} - 272 q^{66} - 158 q^{67} - 360 q^{68} - 384 q^{69} - 296 q^{70} - 174 q^{71} - 368 q^{72} - 472 q^{73} - 352 q^{74} - 214 q^{75} - 320 q^{76} - 352 q^{77} - 400 q^{78} - 246 q^{79} - 312 q^{80} - 182 q^{81} - 320 q^{82} - 282 q^{83} - 688 q^{84} - 352 q^{85} - 280 q^{86} - 350 q^{87} - 328 q^{88} - 504 q^{89} - 344 q^{90} - 334 q^{91} - 248 q^{92} - 296 q^{93} - 344 q^{94} - 358 q^{95} - 328 q^{96} - 840 q^{97} - 280 q^{98} - 342 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2656))\)

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
2656.2.a \(\chi_{2656}(1, \cdot)\) 2656.2.a.a 1 1
2656.2.a.b 1
2656.2.a.c 1
2656.2.a.d 1
2656.2.a.e 1
2656.2.a.f 1
2656.2.a.g 2
2656.2.a.h 2
2656.2.a.i 3
2656.2.a.j 3
2656.2.a.k 4
2656.2.a.l 4
2656.2.a.m 5
2656.2.a.n 5
2656.2.a.o 5
2656.2.a.p 5
2656.2.a.q 8
2656.2.a.r 8
2656.2.a.s 11
2656.2.a.t 11
2656.2.b \(\chi_{2656}(2655, \cdot)\) 2656.2.b.a 84 1
2656.2.c \(\chi_{2656}(1329, \cdot)\) 2656.2.c.a 82 1
2656.2.h \(\chi_{2656}(1327, \cdot)\) 2656.2.h.a 2 1
2656.2.h.b 80
2656.2.j \(\chi_{2656}(665, \cdot)\) None 0 2
2656.2.l \(\chi_{2656}(663, \cdot)\) None 0 2
2656.2.m \(\chi_{2656}(331, \cdot)\) n/a 1336 4
2656.2.n \(\chi_{2656}(333, \cdot)\) n/a 1312 4
2656.2.q \(\chi_{2656}(33, \cdot)\) n/a 3360 40
2656.2.r \(\chi_{2656}(15, \cdot)\) n/a 3280 40
2656.2.w \(\chi_{2656}(17, \cdot)\) n/a 3280 40
2656.2.x \(\chi_{2656}(159, \cdot)\) n/a 3360 40
2656.2.y \(\chi_{2656}(39, \cdot)\) None 0 80
2656.2.ba \(\chi_{2656}(9, \cdot)\) None 0 80
2656.2.be \(\chi_{2656}(21, \cdot)\) n/a 53440 160
2656.2.bf \(\chi_{2656}(19, \cdot)\) n/a 53440 160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2656))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2656)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(83))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(166))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(332))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(664))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1328))\)\(^{\oplus 2}\)