↑

Properties

Label 49.12
Level 49
Weight 12
Dimension 1011
Nonzero newspaces 4
Newform subspaces 20
Sturm bound 2352
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 49 = 7^{2} \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 20 \)
Sturm bound: \(2352\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(49))\).

Total New Old
Modular forms 1108 1060 48
Cusp forms 1048 1011 37
Eisenstein series 60 49 11

Trace form

\( 1011 q - 39 q^{2} - 249 q^{3} - 9679 q^{4} + 20001 q^{5} - 99369 q^{6} + 34034 q^{7} + 30219 q^{8} - 422382 q^{9} + O(q^{10}) \) \( 1011 q - 39 q^{2} - 249 q^{3} - 9679 q^{4} + 20001 q^{5} - 99369 q^{6} + 34034 q^{7} + 30219 q^{8} - 422382 q^{9} - 1960641 q^{10} + 3979023 q^{11} - 2179737 q^{12} - 2214275 q^{13} + 3102834 q^{14} + 17791569 q^{15} - 7339447 q^{16} - 5787387 q^{17} - 11737923 q^{18} - 29051993 q^{19} + 43285515 q^{20} - 44895711 q^{21} - 104881119 q^{22} + 129582435 q^{23} + 363919671 q^{24} - 77027920 q^{25} - 236257917 q^{26} - 342388701 q^{27} - 182520730 q^{28} + 255706107 q^{29} + 1291121391 q^{30} + 528291403 q^{31} + 1209804957 q^{32} - 1388602185 q^{33} - 3778149057 q^{34} - 1015114863 q^{35} - 123859305 q^{36} + 6633112349 q^{37} + 841280331 q^{38} - 2656590510 q^{39} - 2278372101 q^{40} - 2770214013 q^{41} + 2535036189 q^{42} - 3739171325 q^{43} + 776690595 q^{44} + 9550684338 q^{45} + 2279197359 q^{46} - 5282672127 q^{47} + 847148634 q^{48} + 7089906572 q^{49} + 1656247074 q^{50} + 25629844023 q^{51} + 1645831187 q^{52} - 14608435773 q^{53} - 71903479209 q^{54} - 24604955910 q^{55} + 63315266364 q^{56} + 37037416155 q^{57} + 82501244055 q^{58} + 15662227101 q^{59} - 100677930045 q^{60} - 39789893890 q^{61} - 49776812901 q^{62} + 7634450922 q^{63} - 19905320137 q^{64} + 46649902047 q^{65} + 89793531663 q^{66} + 89270723527 q^{67} - 90636034713 q^{68} - 83979136749 q^{69} - 54639604383 q^{70} + 60792136257 q^{71} + 103750539885 q^{72} + 33303884029 q^{73} - 66356605989 q^{74} - 38742651321 q^{75} + 82592362951 q^{76} + 56035238553 q^{77} - 141684970119 q^{78} - 31970903381 q^{79} + 174215903676 q^{80} + 409858132134 q^{81} - 77235483696 q^{82} - 473202116709 q^{83} - 901647043290 q^{84} - 183298377495 q^{85} + 290572892154 q^{86} + 726694143195 q^{87} + 903173819964 q^{88} + 612408645249 q^{89} - 106700878110 q^{90} - 393552473279 q^{91} - 839751804030 q^{92} - 2234126140533 q^{93} - 1484664523920 q^{94} + 353123649963 q^{95} + 3287637834306 q^{96} + 1825844179264 q^{97} + 2748064347756 q^{98} + 482795945736 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(49))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
49.12.a \(\chi_{49}(1, \cdot)\) 49.12.a.a 1 1
49.12.a.b 1
49.12.a.c 2
49.12.a.d 3
49.12.a.e 4
49.12.a.f 6
49.12.a.g 6
49.12.a.h 12
49.12.c \(\chi_{49}(18, \cdot)\) 49.12.c.a 2 2
49.12.c.b 2
49.12.c.c 2
49.12.c.d 4
49.12.c.e 4
49.12.c.f 6
49.12.c.g 6
49.12.c.h 8
49.12.c.i 12
49.12.c.j 24
49.12.e \(\chi_{49}(8, \cdot)\) 49.12.e.a 306 6
49.12.g \(\chi_{49}(2, \cdot)\) 49.12.g.a 600 12

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(49))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(49)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)