Properties

Label 49.6
Level 49
Weight 6
Dimension 446
Nonzero newspaces 4
Newform subspaces 17
Sturm bound 1176
Trace bound 1

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Defining parameters

Level: \( N \) = \( 49 = 7^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 17 \)
Sturm bound: \(1176\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(49))\).

Total New Old
Modular forms 520 495 25
Cusp forms 460 446 14
Eisenstein series 60 49 11

Trace form

\( 446 q - 15 q^{2} + 3 q^{3} - 143 q^{4} + 51 q^{5} + 423 q^{6} + 98 q^{7} + 315 q^{8} - 1803 q^{9} + O(q^{10}) \) \( 446 q - 15 q^{2} + 3 q^{3} - 143 q^{4} + 51 q^{5} + 423 q^{6} + 98 q^{7} + 315 q^{8} - 1803 q^{9} - 3105 q^{10} - 429 q^{11} + 4599 q^{12} + 4655 q^{13} + 1722 q^{14} - 1863 q^{15} - 7223 q^{16} - 4869 q^{17} - 7611 q^{18} + 5987 q^{19} + 9387 q^{20} + 1113 q^{21} - 399 q^{22} - 7869 q^{23} - 3609 q^{24} + 10177 q^{25} - 4557 q^{26} - 6885 q^{27} + 518 q^{28} + 7941 q^{29} + 39711 q^{30} + 22403 q^{31} + 1485 q^{32} - 40353 q^{33} - 76017 q^{34} - 29379 q^{35} - 80505 q^{36} - 41721 q^{37} + 66867 q^{38} + 108654 q^{39} + 235083 q^{40} + 115689 q^{41} + 143997 q^{42} + 66503 q^{43} + 31875 q^{44} - 106716 q^{45} - 224025 q^{46} - 174879 q^{47} - 442278 q^{48} - 201544 q^{49} - 241350 q^{50} - 173817 q^{51} - 118125 q^{52} + 5325 q^{53} + 426207 q^{54} + 483270 q^{55} + 484092 q^{56} + 217419 q^{57} + 215031 q^{58} + 100089 q^{59} + 117075 q^{60} - 73176 q^{61} - 229821 q^{62} - 362838 q^{63} - 258473 q^{64} - 100149 q^{65} - 250401 q^{66} + 131843 q^{67} + 275079 q^{68} + 237219 q^{69} + 130473 q^{70} - 68919 q^{71} - 116307 q^{72} - 272101 q^{73} - 389589 q^{74} - 151917 q^{75} - 116473 q^{76} - 73395 q^{77} - 64743 q^{78} - 148093 q^{79} - 857700 q^{80} - 515355 q^{81} - 317016 q^{82} + 517167 q^{83} + 1595286 q^{84} + 830997 q^{85} + 2040834 q^{86} + 1815267 q^{87} + 1842588 q^{88} + 305223 q^{89} + 431178 q^{90} - 104279 q^{91} - 830574 q^{92} - 1071189 q^{93} - 1142040 q^{94} - 1783173 q^{95} - 3666558 q^{96} - 1551466 q^{97} - 2833740 q^{98} - 1126668 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(49))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
49.6.a \(\chi_{49}(1, \cdot)\) 49.6.a.a 1 1
49.6.a.b 1
49.6.a.c 2
49.6.a.d 2
49.6.a.e 2
49.6.a.f 2
49.6.a.g 4
49.6.c \(\chi_{49}(18, \cdot)\) 49.6.c.a 2 2
49.6.c.b 2
49.6.c.c 2
49.6.c.d 4
49.6.c.e 4
49.6.c.f 4
49.6.c.g 4
49.6.c.h 8
49.6.e \(\chi_{49}(8, \cdot)\) 49.6.e.a 138 6
49.6.g \(\chi_{49}(2, \cdot)\) 49.6.g.a 264 12

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(49))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(49)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)