Properties

Label 1014.3
Level 1014
Weight 3
Dimension 14028
Nonzero newspaces 12
Sturm bound 170352
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(170352\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1014))\).

Total New Old
Modular forms 57696 14028 43668
Cusp forms 55872 14028 41844
Eisenstein series 1824 0 1824

Trace form

\( 14028 q - 80 q^{7} - 48 q^{8} - 24 q^{9} + O(q^{10}) \) \( 14028 q - 80 q^{7} - 48 q^{8} - 24 q^{9} - 120 q^{10} - 48 q^{11} + 48 q^{13} + 96 q^{14} + 144 q^{15} + 64 q^{16} + 144 q^{17} + 72 q^{18} + 160 q^{19} + 96 q^{20} - 120 q^{21} - 96 q^{23} + 144 q^{27} + 240 q^{29} + 384 q^{30} + 288 q^{31} + 744 q^{33} + 480 q^{35} + 96 q^{36} + 144 q^{37} - 96 q^{39} - 120 q^{41} - 288 q^{42} - 512 q^{43} - 912 q^{45} - 192 q^{47} - 32 q^{49} - 168 q^{50} - 1248 q^{51} - 72 q^{52} - 960 q^{53} - 720 q^{54} - 912 q^{55} - 384 q^{56} - 792 q^{57} - 648 q^{58} - 336 q^{59} - 192 q^{60} + 312 q^{61} - 288 q^{62} + 600 q^{63} + 180 q^{65} + 192 q^{66} + 832 q^{67} + 48 q^{68} + 1416 q^{69} + 864 q^{70} + 672 q^{71} + 384 q^{72} + 1024 q^{73} + 312 q^{74} + 720 q^{75} - 320 q^{76} + 216 q^{78} - 672 q^{79} + 192 q^{80} + 360 q^{81} - 1320 q^{82} - 1008 q^{83} - 336 q^{84} - 1656 q^{85} - 384 q^{86} - 1392 q^{87} - 864 q^{89} + 104 q^{91} + 192 q^{92} - 1320 q^{93} + 960 q^{94} + 960 q^{95} + 2640 q^{97} + 768 q^{98} + 1224 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1014))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1014.3.c \(\chi_{1014}(677, \cdot)\) n/a 104 1
1014.3.d \(\chi_{1014}(1013, \cdot)\) n/a 104 1
1014.3.f \(\chi_{1014}(577, \cdot)\) 1014.3.f.a 4 2
1014.3.f.b 4
1014.3.f.c 4
1014.3.f.d 4
1014.3.f.e 4
1014.3.f.f 4
1014.3.f.g 4
1014.3.f.h 8
1014.3.f.i 8
1014.3.f.j 8
1014.3.f.k 24
1014.3.f.l 24
1014.3.h \(\chi_{1014}(191, \cdot)\) n/a 204 2
1014.3.j \(\chi_{1014}(23, \cdot)\) n/a 204 2
1014.3.l \(\chi_{1014}(19, \cdot)\) n/a 208 4
1014.3.n \(\chi_{1014}(77, \cdot)\) n/a 1440 12
1014.3.o \(\chi_{1014}(53, \cdot)\) n/a 1440 12
1014.3.s \(\chi_{1014}(31, \cdot)\) n/a 1488 24
1014.3.t \(\chi_{1014}(17, \cdot)\) n/a 2928 24
1014.3.v \(\chi_{1014}(29, \cdot)\) n/a 2928 24
1014.3.w \(\chi_{1014}(7, \cdot)\) n/a 2880 48

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1014))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1014)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 2}\)