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Properties

Label 415.2
Level 415
Weight 2
Dimension 6067
Nonzero newspaces 6
Newform subspaces 11
Sturm bound 27552
Trace bound 1

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Defining parameters

Level: \( N \) = \( 415 = 5 \cdot 83 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 11 \)
Sturm bound: \(27552\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(415))\).

Total New Old
Modular forms 7216 6555 661
Cusp forms 6561 6067 494
Eisenstein series 655 488 167

Trace form

\( 6067 q - 85 q^{2} - 86 q^{3} - 89 q^{4} - 124 q^{5} - 258 q^{6} - 90 q^{7} - 97 q^{8} - 95 q^{9} + O(q^{10}) \) \( 6067 q - 85 q^{2} - 86 q^{3} - 89 q^{4} - 124 q^{5} - 258 q^{6} - 90 q^{7} - 97 q^{8} - 95 q^{9} - 126 q^{10} - 258 q^{11} - 110 q^{12} - 96 q^{13} - 106 q^{14} - 127 q^{15} - 277 q^{16} - 100 q^{17} - 121 q^{18} - 102 q^{19} - 130 q^{20} - 278 q^{21} - 118 q^{22} - 106 q^{23} - 142 q^{24} - 124 q^{25} - 288 q^{26} - 122 q^{27} - 138 q^{28} - 112 q^{29} - 135 q^{30} - 278 q^{31} - 145 q^{32} - 130 q^{33} - 136 q^{34} - 131 q^{35} - 337 q^{36} - 120 q^{37} - 142 q^{38} - 138 q^{39} - 138 q^{40} - 288 q^{41} - 178 q^{42} - 126 q^{43} - 166 q^{44} - 136 q^{45} - 318 q^{46} - 130 q^{47} - 206 q^{48} - 139 q^{49} - 126 q^{50} - 318 q^{51} - 180 q^{52} - 136 q^{53} - 202 q^{54} - 135 q^{55} - 366 q^{56} - 162 q^{57} - 172 q^{58} - 142 q^{59} - 151 q^{60} - 308 q^{61} - 178 q^{62} - 186 q^{63} - 209 q^{64} - 137 q^{65} - 308 q^{66} - 68 q^{67} + 120 q^{68} + 68 q^{69} + 17 q^{70} - 236 q^{71} + 543 q^{72} + 90 q^{73} - 32 q^{74} + 160 q^{75} - 58 q^{76} + 68 q^{77} + 570 q^{78} + 84 q^{79} + 256 q^{80} - 39 q^{81} + 202 q^{82} + 81 q^{83} + 596 q^{84} - 18 q^{85} - 50 q^{86} + 126 q^{87} + 558 q^{88} + 74 q^{89} + 248 q^{90} - 112 q^{91} + 78 q^{92} + 364 q^{93} - 62 q^{94} - 20 q^{95} + 322 q^{96} - 98 q^{97} + 75 q^{98} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(415))\)

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
415.2.a \(\chi_{415}(1, \cdot)\) 415.2.a.a 1 1
415.2.a.b 2
415.2.a.c 6
415.2.a.d 7
415.2.a.e 11
415.2.b \(\chi_{415}(84, \cdot)\) 415.2.b.a 40 1
415.2.e \(\chi_{415}(82, \cdot)\) 415.2.e.a 80 2
415.2.g \(\chi_{415}(11, \cdot)\) 415.2.g.a 520 40
415.2.g.b 600
415.2.j \(\chi_{415}(4, \cdot)\) 415.2.j.a 1600 40
415.2.l \(\chi_{415}(2, \cdot)\) 415.2.l.a 3200 80

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(415))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(415)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(83))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(415))\)\(^{\oplus 1}\)