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Properties

Label 803.2
Level 803
Weight 2
Dimension 25545
Nonzero newspaces 24
Newform subspaces 33
Sturm bound 106560
Trace bound 5

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Defining parameters

Level: \( N \) = \( 803 = 11 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Newform subspaces: \( 33 \)
Sturm bound: \(106560\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(803))\).

Total New Old
Modular forms 27360 26825 535
Cusp forms 25921 25545 376
Eisenstein series 1439 1280 159

Trace form

\( 25545 q - 287 q^{2} - 290 q^{3} - 299 q^{4} - 296 q^{5} - 304 q^{6} - 292 q^{7} - 303 q^{8} - 297 q^{9} + O(q^{10}) \) \( 25545 q - 287 q^{2} - 290 q^{3} - 299 q^{4} - 296 q^{5} - 304 q^{6} - 292 q^{7} - 303 q^{8} - 297 q^{9} - 302 q^{10} - 327 q^{11} - 672 q^{12} - 310 q^{13} - 320 q^{14} - 310 q^{15} - 311 q^{16} - 302 q^{17} - 335 q^{18} - 308 q^{19} - 334 q^{20} - 324 q^{21} - 323 q^{22} - 670 q^{23} - 348 q^{24} - 311 q^{25} - 314 q^{26} - 338 q^{27} - 336 q^{28} - 318 q^{29} - 364 q^{30} - 334 q^{31} - 367 q^{32} - 326 q^{33} - 710 q^{34} - 332 q^{35} - 371 q^{36} - 332 q^{37} - 348 q^{38} - 336 q^{39} - 378 q^{40} - 314 q^{41} - 376 q^{42} - 320 q^{43} - 335 q^{44} - 722 q^{45} - 364 q^{46} - 352 q^{47} - 420 q^{48} - 339 q^{49} - 397 q^{50} - 364 q^{51} - 402 q^{52} - 330 q^{53} - 388 q^{54} - 332 q^{55} - 768 q^{56} - 344 q^{57} - 198 q^{58} - 286 q^{59} - 20 q^{60} - 230 q^{61} - 212 q^{62} - 40 q^{63} + 129 q^{64} - 164 q^{65} - 196 q^{66} - 390 q^{67} + 134 q^{68} - 242 q^{69} + 136 q^{70} - 138 q^{71} + 237 q^{72} - 77 q^{73} - 390 q^{74} - 132 q^{75} + 220 q^{76} - 220 q^{77} - 256 q^{78} - 204 q^{79} + 74 q^{80} - 99 q^{81} - 158 q^{82} - 144 q^{83} + 8 q^{84} - 32 q^{85} - 300 q^{86} - 264 q^{87} - 123 q^{88} - 696 q^{89} - 350 q^{90} - 360 q^{91} - 452 q^{92} - 402 q^{93} - 400 q^{94} - 408 q^{95} - 524 q^{96} - 372 q^{97} - 471 q^{98} - 333 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(803))\)

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
803.2.a \(\chi_{803}(1, \cdot)\) 803.2.a.a 2 1
803.2.a.b 5
803.2.a.c 9
803.2.a.d 10
803.2.a.e 16
803.2.a.f 19
803.2.d \(\chi_{803}(364, \cdot)\) 803.2.d.a 2 1
803.2.d.b 62
803.2.e \(\chi_{803}(210, \cdot)\) 803.2.e.a 64 2
803.2.e.b 64
803.2.g \(\chi_{803}(100, \cdot)\) 803.2.g.a 124 2
803.2.h \(\chi_{803}(147, \cdot)\) 803.2.h.a 136 4
803.2.h.b 152
803.2.i \(\chi_{803}(155, \cdot)\) 803.2.i.a 128 2
803.2.l \(\chi_{803}(10, \cdot)\) 803.2.l.a 288 4
803.2.n \(\chi_{803}(89, \cdot)\) 803.2.n.a 186 6
803.2.n.b 186
803.2.o \(\chi_{803}(218, \cdot)\) 803.2.o.a 288 4
803.2.r \(\chi_{803}(122, \cdot)\) 803.2.r.a 248 4
803.2.t \(\chi_{803}(64, \cdot)\) 803.2.t.a 576 8
803.2.v \(\chi_{803}(144, \cdot)\) 803.2.v.a 372 6
803.2.x \(\chi_{803}(27, \cdot)\) 803.2.x.a 576 8
803.2.ba \(\chi_{803}(21, \cdot)\) 803.2.ba.a 576 8
803.2.bd \(\chi_{803}(9, \cdot)\) 803.2.bd.a 576 8
803.2.be \(\chi_{803}(12, \cdot)\) 803.2.be.a 720 12
803.2.bh \(\chi_{803}(51, \cdot)\) 803.2.bh.a 1152 16
803.2.bi \(\chi_{803}(4, \cdot)\) 803.2.bi.a 1728 24
803.2.bk \(\chi_{803}(3, \cdot)\) 803.2.bk.a 1152 16
803.2.bm \(\chi_{803}(87, \cdot)\) 803.2.bm.a 1728 24
803.2.bo \(\chi_{803}(36, \cdot)\) 803.2.bo.a 1728 24
803.2.bq \(\chi_{803}(7, \cdot)\) 803.2.bq.a 2304 32
803.2.bt \(\chi_{803}(25, \cdot)\) 803.2.bt.a 3456 48
803.2.bu \(\chi_{803}(13, \cdot)\) 803.2.bu.a 6912 96

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(803))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(803)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(73))\)\(^{\oplus 2}\)