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Properties

Label 753.2
Level 753
Weight 2
Dimension 15499
Nonzero newspaces 8
Newform subspaces 21
Sturm bound 84000
Trace bound 1

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Defining parameters

Level: \( N \) = \( 753 = 3 \cdot 251 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 21 \)
Sturm bound: \(84000\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(753))\).

Total New Old
Modular forms 21500 15999 5501
Cusp forms 20501 15499 5002
Eisenstein series 999 500 499

Trace form

\( 15499 q - 3 q^{2} - 126 q^{3} - 257 q^{4} - 6 q^{5} - 128 q^{6} - 258 q^{7} - 15 q^{8} - 126 q^{9} + O(q^{10}) \) \( 15499 q - 3 q^{2} - 126 q^{3} - 257 q^{4} - 6 q^{5} - 128 q^{6} - 258 q^{7} - 15 q^{8} - 126 q^{9} - 268 q^{10} - 12 q^{11} - 132 q^{12} - 264 q^{13} - 24 q^{14} - 131 q^{15} - 281 q^{16} - 18 q^{17} - 128 q^{18} - 270 q^{19} - 42 q^{20} - 133 q^{21} - 286 q^{22} - 24 q^{23} - 140 q^{24} - 281 q^{25} - 42 q^{26} - 126 q^{27} - 306 q^{28} - 30 q^{29} - 143 q^{30} - 282 q^{31} - 63 q^{32} - 137 q^{33} - 304 q^{34} - 48 q^{35} - 132 q^{36} - 288 q^{37} - 60 q^{38} - 139 q^{39} - 340 q^{40} - 42 q^{41} - 149 q^{42} - 294 q^{43} - 84 q^{44} - 131 q^{45} - 322 q^{46} - 48 q^{47} - 156 q^{48} - 307 q^{49} - 93 q^{50} - 143 q^{51} - 348 q^{52} - 54 q^{53} - 128 q^{54} - 322 q^{55} - 120 q^{56} - 145 q^{57} - 340 q^{58} - 60 q^{59} - 167 q^{60} - 312 q^{61} - 96 q^{62} - 133 q^{63} - 377 q^{64} - 84 q^{65} - 161 q^{66} - 318 q^{67} - 126 q^{68} - 149 q^{69} - 394 q^{70} - 72 q^{71} - 140 q^{72} - 324 q^{73} - 114 q^{74} - 156 q^{75} - 390 q^{76} - 96 q^{77} - 167 q^{78} - 330 q^{79} - 186 q^{80} - 126 q^{81} - 376 q^{82} - 84 q^{83} - 181 q^{84} - 358 q^{85} - 132 q^{86} - 155 q^{87} - 430 q^{88} - 90 q^{89} - 143 q^{90} - 362 q^{91} - 168 q^{92} - 157 q^{93} - 394 q^{94} - 120 q^{95} - 188 q^{96} - 348 q^{97} - 171 q^{98} - 137 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(753))\)

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
753.2.a \(\chi_{753}(1, \cdot)\) 753.2.a.a 1 1
753.2.a.b 1
753.2.a.c 1
753.2.a.d 2
753.2.a.e 4
753.2.a.f 6
753.2.a.g 6
753.2.a.h 9
753.2.a.i 11
753.2.d \(\chi_{753}(752, \cdot)\) 753.2.d.a 14 1
753.2.d.b 68
753.2.e \(\chi_{753}(271, \cdot)\) 753.2.e.a 4 4
753.2.e.b 80
753.2.e.c 84
753.2.h \(\chi_{753}(32, \cdot)\) 753.2.h.a 328 4
753.2.i \(\chi_{753}(4, \cdot)\) 753.2.i.a 420 20
753.2.i.b 420
753.2.j \(\chi_{753}(2, \cdot)\) 753.2.j.a 1640 20
753.2.m \(\chi_{753}(7, \cdot)\) 753.2.m.a 2100 100
753.2.m.b 2100
753.2.o \(\chi_{753}(11, \cdot)\) 753.2.o.a 8200 100

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(753))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(753)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(251))\)\(^{\oplus 2}\)