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Properties

Label 414.3
Level 414
Weight 3
Dimension 2496
Nonzero newspaces 8
Newform subspaces 14
Sturm bound 28512
Trace bound 3

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Defining parameters

Level: \( N \) = \( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 14 \)
Sturm bound: \(28512\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(414))\).

Total New Old
Modular forms 9856 2496 7360
Cusp forms 9152 2496 6656
Eisenstein series 704 0 704

Trace form

\( 2496 q + 36 q^{5} + 24 q^{6} + 12 q^{7} - 24 q^{9} + O(q^{10}) \) \( 2496 q + 36 q^{5} + 24 q^{6} + 12 q^{7} - 24 q^{9} - 24 q^{10} - 36 q^{11} - 24 q^{12} - 12 q^{13} - 72 q^{14} - 36 q^{15} - 110 q^{17} + 48 q^{18} + 78 q^{19} + 28 q^{20} + 84 q^{21} + 120 q^{22} + 26 q^{23} + 96 q^{25} + 88 q^{26} + 84 q^{28} + 118 q^{29} - 144 q^{30} - 54 q^{31} - 108 q^{33} - 120 q^{34} - 220 q^{35} - 24 q^{36} - 472 q^{37} + 144 q^{38} + 204 q^{39} + 48 q^{40} + 164 q^{41} + 96 q^{42} + 164 q^{43} + 108 q^{45} - 24 q^{46} - 20 q^{47} - 48 q^{48} + 420 q^{49} + 144 q^{51} + 24 q^{52} + 176 q^{53} + 544 q^{54} + 2084 q^{55} + 648 q^{56} + 1164 q^{57} + 1296 q^{58} + 2432 q^{59} + 424 q^{60} + 1524 q^{61} + 1188 q^{62} + 656 q^{63} + 96 q^{64} + 1206 q^{65} + 496 q^{66} + 312 q^{67} - 144 q^{68} - 238 q^{69} - 216 q^{70} - 990 q^{71} - 160 q^{72} - 180 q^{73} - 1728 q^{74} - 2132 q^{75} - 48 q^{76} - 2790 q^{77} - 1608 q^{78} - 2892 q^{79} - 792 q^{80} - 1784 q^{81} - 1872 q^{82} - 2390 q^{83} - 416 q^{84} - 2376 q^{85} - 972 q^{86} + 108 q^{87} - 240 q^{88} - 44 q^{89} - 696 q^{91} - 36 q^{92} - 444 q^{93} - 648 q^{94} - 602 q^{95} - 96 q^{96} - 1722 q^{97} - 704 q^{98} - 252 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(414))\)

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
414.3.b \(\chi_{414}(91, \cdot)\) 414.3.b.a 4 1
414.3.b.b 8
414.3.b.c 8
414.3.c \(\chi_{414}(323, \cdot)\) 414.3.c.a 4 1
414.3.c.b 8
414.3.g \(\chi_{414}(47, \cdot)\) 414.3.g.a 88 2
414.3.h \(\chi_{414}(229, \cdot)\) 414.3.h.a 96 2
414.3.k \(\chi_{414}(35, \cdot)\) 414.3.k.a 80 10
414.3.k.b 80
414.3.l \(\chi_{414}(19, \cdot)\) 414.3.l.a 40 10
414.3.l.b 80
414.3.l.c 80
414.3.n \(\chi_{414}(7, \cdot)\) 414.3.n.a 960 20
414.3.o \(\chi_{414}(29, \cdot)\) 414.3.o.a 960 20

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(414))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(414)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 2}\)