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Properties

Label 49.3
Level 49
Weight 3
Dimension 164
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 588
Trace bound 1

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Defining parameters

Level: \( N \) = \( 49 = 7^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(588\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(49))\).

Total New Old
Modular forms 226 212 14
Cusp forms 166 164 2
Eisenstein series 60 48 12

Trace form

\( 164 q - 15 q^{2} - 21 q^{3} - 31 q^{4} - 21 q^{5} - 21 q^{6} - 14 q^{7} - 33 q^{8} - 39 q^{9} + O(q^{10}) \) \( 164 q - 15 q^{2} - 21 q^{3} - 31 q^{4} - 21 q^{5} - 21 q^{6} - 14 q^{7} - 33 q^{8} - 39 q^{9} - 21 q^{10} - 9 q^{11} - 21 q^{12} - 21 q^{13} - 42 q^{14} - 39 q^{15} + q^{16} - 21 q^{17} + 33 q^{18} - 21 q^{19} - 21 q^{20} - 21 q^{21} - 75 q^{22} - 57 q^{23} - 21 q^{24} - 71 q^{25} - 21 q^{26} - 21 q^{27} + 14 q^{28} + 69 q^{29} - 21 q^{30} - 21 q^{31} - 111 q^{32} - 21 q^{33} - 21 q^{34} - 21 q^{35} + 195 q^{36} + 363 q^{37} + 399 q^{38} + 420 q^{39} + 987 q^{40} + 273 q^{41} + 483 q^{42} + 55 q^{43} + 543 q^{44} + 294 q^{45} + 339 q^{46} + 21 q^{47} - 154 q^{49} - 78 q^{50} - 273 q^{51} - 637 q^{52} - 219 q^{53} - 777 q^{54} - 756 q^{55} - 1050 q^{56} - 417 q^{57} - 1185 q^{58} - 483 q^{59} - 1533 q^{60} - 658 q^{61} - 609 q^{62} - 378 q^{63} - 433 q^{64} - 21 q^{65} - 21 q^{66} + 215 q^{67} - 21 q^{68} - 21 q^{69} - 21 q^{70} - 267 q^{71} + 33 q^{72} - 21 q^{73} - 249 q^{74} - 21 q^{75} - 21 q^{76} - 63 q^{77} + 609 q^{78} + 167 q^{79} + 1050 q^{80} + 1161 q^{81} + 1554 q^{82} + 1155 q^{83} + 2982 q^{84} + 969 q^{85} + 1944 q^{86} + 1659 q^{87} + 2022 q^{88} + 651 q^{89} + 2772 q^{90} + 483 q^{91} + 516 q^{92} + 987 q^{93} + 546 q^{94} + 315 q^{95} + 420 q^{96} - 168 q^{98} - 288 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(49))\)

We only show spaces with odd 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
49.3.b \(\chi_{49}(48, \cdot)\) 49.3.b.a 4 1
49.3.d \(\chi_{49}(19, \cdot)\) 49.3.d.a 2 2
49.3.d.b 8
49.3.f \(\chi_{49}(6, \cdot)\) 49.3.f.a 54 6
49.3.h \(\chi_{49}(3, \cdot)\) 49.3.h.a 96 12

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(49))\) into lower level spaces

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