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Properties

Label 959.2
Level 959
Weight 2
Dimension 35291
Nonzero newspaces 16
Newform subspaces 29
Sturm bound 150144
Trace bound 3

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Defining parameters

Level: \( N \) = \( 959 = 7 \cdot 137 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 29 \)
Sturm bound: \(150144\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(959))\).

Total New Old
Modular forms 38352 36643 1709
Cusp forms 36721 35291 1430
Eisenstein series 1631 1352 279

Trace form

\( 35291 q - 275 q^{2} - 276 q^{3} - 279 q^{4} - 278 q^{5} - 284 q^{6} - 341 q^{7} - 695 q^{8} - 285 q^{9} + O(q^{10}) \) \( 35291 q - 275 q^{2} - 276 q^{3} - 279 q^{4} - 278 q^{5} - 284 q^{6} - 341 q^{7} - 695 q^{8} - 285 q^{9} - 290 q^{10} - 284 q^{11} - 300 q^{12} - 286 q^{13} - 343 q^{14} - 704 q^{15} - 303 q^{16} - 290 q^{17} - 311 q^{18} - 292 q^{19} - 314 q^{20} - 344 q^{21} - 716 q^{22} - 296 q^{23} - 332 q^{24} - 303 q^{25} - 314 q^{26} - 312 q^{27} - 347 q^{28} - 710 q^{29} - 344 q^{30} - 304 q^{31} - 335 q^{32} - 320 q^{33} - 326 q^{34} - 346 q^{35} - 771 q^{36} - 310 q^{37} - 332 q^{38} - 328 q^{39} - 362 q^{40} - 314 q^{41} - 352 q^{42} - 724 q^{43} - 356 q^{44} - 350 q^{45} - 344 q^{46} - 320 q^{47} - 396 q^{48} - 341 q^{49} - 773 q^{50} - 344 q^{51} - 370 q^{52} - 326 q^{53} - 392 q^{54} - 344 q^{55} - 355 q^{56} - 760 q^{57} - 362 q^{58} - 332 q^{59} - 440 q^{60} - 334 q^{61} - 368 q^{62} - 353 q^{63} - 807 q^{64} - 356 q^{65} - 416 q^{66} - 340 q^{67} - 398 q^{68} - 368 q^{69} - 358 q^{70} - 752 q^{71} - 467 q^{72} - 346 q^{73} - 386 q^{74} - 396 q^{75} - 412 q^{76} - 352 q^{77} - 848 q^{78} - 352 q^{79} - 458 q^{80} - 393 q^{81} - 398 q^{82} - 356 q^{83} - 368 q^{84} - 788 q^{85} - 404 q^{86} - 392 q^{87} - 452 q^{88} - 362 q^{89} - 506 q^{90} - 354 q^{91} - 848 q^{92} - 400 q^{93} - 416 q^{94} - 392 q^{95} - 524 q^{96} - 370 q^{97} - 343 q^{98} - 836 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(959))\)

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
959.2.a \(\chi_{959}(1, \cdot)\) 959.2.a.a 2 1
959.2.a.b 7
959.2.a.c 10
959.2.a.d 24
959.2.a.e 26
959.2.c \(\chi_{959}(547, \cdot)\) 959.2.c.a 2 1
959.2.c.b 32
959.2.c.c 36
959.2.e \(\chi_{959}(275, \cdot)\) 959.2.e.a 90 2
959.2.e.b 90
959.2.f \(\chi_{959}(722, \cdot)\) 959.2.f.a 66 2
959.2.f.b 70
959.2.i \(\chi_{959}(410, \cdot)\) 959.2.i.a 180 2
959.2.k \(\chi_{959}(41, \cdot)\) 959.2.k.a 8 4
959.2.k.b 352
959.2.n \(\chi_{959}(37, \cdot)\) 959.2.n.a 360 4
959.2.o \(\chi_{959}(50, \cdot)\) 959.2.o.a 544 16
959.2.o.b 576
959.2.p \(\chi_{959}(10, \cdot)\) 959.2.p.a 720 8
959.2.s \(\chi_{959}(15, \cdot)\) 959.2.s.a 544 16
959.2.s.b 576
959.2.u \(\chi_{959}(16, \cdot)\) 959.2.u.a 2880 32
959.2.w \(\chi_{959}(8, \cdot)\) 959.2.w.a 1056 32
959.2.w.b 1120
959.2.y \(\chi_{959}(4, \cdot)\) 959.2.y.a 2880 32
959.2.bb \(\chi_{959}(6, \cdot)\) 959.2.bb.a 128 64
959.2.bb.b 5632
959.2.bc \(\chi_{959}(2, \cdot)\) 959.2.bc.a 5760 64
959.2.bf \(\chi_{959}(3, \cdot)\) 959.2.bf.a 11520 128

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(959))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(959)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(137))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(959))\)\(^{\oplus 1}\)