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Properties

Label 751.2
Level 751
Weight 2
Dimension 23126
Nonzero newspaces 8
Newform subspaces 11
Sturm bound 94000
Trace bound 1

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Defining parameters

Level: \( N \) = \( 751 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 11 \)
Sturm bound: \(94000\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(751))\).

Total New Old
Modular forms 23875 23875 0
Cusp forms 23126 23126 0
Eisenstein series 749 749 0

Trace form

\( 23126 q - 372 q^{2} - 371 q^{3} - 368 q^{4} - 369 q^{5} - 363 q^{6} - 367 q^{7} - 360 q^{8} - 362 q^{9} + O(q^{10}) \) \( 23126 q - 372 q^{2} - 371 q^{3} - 368 q^{4} - 369 q^{5} - 363 q^{6} - 367 q^{7} - 360 q^{8} - 362 q^{9} - 357 q^{10} - 363 q^{11} - 347 q^{12} - 361 q^{13} - 351 q^{14} - 351 q^{15} - 344 q^{16} - 357 q^{17} - 336 q^{18} - 355 q^{19} - 333 q^{20} - 343 q^{21} - 339 q^{22} - 351 q^{23} - 315 q^{24} - 344 q^{25} - 333 q^{26} - 335 q^{27} - 319 q^{28} - 345 q^{29} - 303 q^{30} - 343 q^{31} - 312 q^{32} - 327 q^{33} - 321 q^{34} - 327 q^{35} - 284 q^{36} - 337 q^{37} - 315 q^{38} - 319 q^{39} - 285 q^{40} - 333 q^{41} - 279 q^{42} - 331 q^{43} - 291 q^{44} - 297 q^{45} - 303 q^{46} - 327 q^{47} - 251 q^{48} - 318 q^{49} - 282 q^{50} - 303 q^{51} - 277 q^{52} - 321 q^{53} - 255 q^{54} - 303 q^{55} - 255 q^{56} - 295 q^{57} - 285 q^{58} - 315 q^{59} - 207 q^{60} - 313 q^{61} - 279 q^{62} - 271 q^{63} - 248 q^{64} - 291 q^{65} - 231 q^{66} - 307 q^{67} - 249 q^{68} - 279 q^{69} - 231 q^{70} - 303 q^{71} - 180 q^{72} - 301 q^{73} - 261 q^{74} - 251 q^{75} - 235 q^{76} - 279 q^{77} - 207 q^{78} - 295 q^{79} - 189 q^{80} - 254 q^{81} - 249 q^{82} - 291 q^{83} - 151 q^{84} - 267 q^{85} - 243 q^{86} - 255 q^{87} - 195 q^{88} - 285 q^{89} - 141 q^{90} - 263 q^{91} - 207 q^{92} - 247 q^{93} - 231 q^{94} - 255 q^{95} - 123 q^{96} - 277 q^{97} - 204 q^{98} - 219 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(751))\)

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
751.2.a \(\chi_{751}(1, \cdot)\) 751.2.a.a 24 1
751.2.a.b 38
751.2.c \(\chi_{751}(72, \cdot)\) 751.2.c.a 124 2
751.2.d \(\chi_{751}(80, \cdot)\) 751.2.d.a 4 4
751.2.d.b 4
751.2.d.c 236
751.2.g \(\chi_{751}(76, \cdot)\) 751.2.g.a 496 8
751.2.h \(\chi_{751}(51, \cdot)\) 751.2.h.a 1220 20
751.2.k \(\chi_{751}(32, \cdot)\) 751.2.k.a 2480 40
751.2.l \(\chi_{751}(8, \cdot)\) 751.2.l.a 6100 100
751.2.o \(\chi_{751}(2, \cdot)\) 751.2.o.a 12400 200