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Properties

Label 2058.2
Level 2058
Weight 2
Dimension 27648
Nonzero newspaces 12
Sturm bound 460992
Trace bound 6

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Defining parameters

Level: \( N \) = \( 2058 = 2 \cdot 3 \cdot 7^{3} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(460992\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2058))\).

Total New Old
Modular forms 117432 27648 89784
Cusp forms 113065 27648 85417
Eisenstein series 4367 0 4367

Trace form

\( 27648 q - 2 q^{3} - 4 q^{4} - 12 q^{5} - 6 q^{6} - 8 q^{9} + O(q^{10}) \) \( 27648 q - 2 q^{3} - 4 q^{4} - 12 q^{5} - 6 q^{6} - 8 q^{9} - 12 q^{10} - 24 q^{11} - 2 q^{12} - 16 q^{13} - 12 q^{17} + 12 q^{18} - 16 q^{19} - 12 q^{23} + 6 q^{24} - 24 q^{25} - 12 q^{26} - 2 q^{27} - 24 q^{29} - 12 q^{30} - 40 q^{31} - 24 q^{33} - 24 q^{34} - 8 q^{36} + 168 q^{37} + 132 q^{38} + 168 q^{39} + 156 q^{40} + 288 q^{41} + 84 q^{42} + 256 q^{43} + 144 q^{44} + 156 q^{45} + 456 q^{46} + 300 q^{47} + 26 q^{48} + 336 q^{49} + 288 q^{50} + 348 q^{51} + 64 q^{52} + 300 q^{53} + 18 q^{54} + 804 q^{55} + 84 q^{56} + 140 q^{57} + 348 q^{58} + 288 q^{59} + 96 q^{60} + 352 q^{61} + 144 q^{62} + 14 q^{63} - 4 q^{64} - 84 q^{65} - 24 q^{67} - 12 q^{68} - 24 q^{69} - 72 q^{71} - 12 q^{72} - 52 q^{73} - 36 q^{74} - 38 q^{75} - 16 q^{76} - 24 q^{78} - 120 q^{79} - 12 q^{80} + 112 q^{81} - 72 q^{82} + 216 q^{83} + 144 q^{85} - 60 q^{86} + 276 q^{87} - 12 q^{88} + 240 q^{89} - 12 q^{90} + 168 q^{91} - 24 q^{92} + 476 q^{93} - 72 q^{94} + 564 q^{95} + 6 q^{96} + 236 q^{97} + 336 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2058))\)

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
2058.2.a \(\chi_{2058}(1, \cdot)\) 2058.2.a.a 3 1
2058.2.a.b 3
2058.2.a.c 3
2058.2.a.d 3
2058.2.a.e 3
2058.2.a.f 3
2058.2.a.g 3
2058.2.a.h 3
2058.2.a.i 3
2058.2.a.j 3
2058.2.a.k 3
2058.2.a.l 3
2058.2.a.m 6
2058.2.a.n 6
2058.2.d \(\chi_{2058}(2057, \cdot)\) 2058.2.d.a 48 1
2058.2.d.b 48
2058.2.e \(\chi_{2058}(361, \cdot)\) 2058.2.e.a 6 2
2058.2.e.b 6
2058.2.e.c 6
2058.2.e.d 6
2058.2.e.e 6
2058.2.e.f 6
2058.2.e.g 6
2058.2.e.h 6
2058.2.e.i 6
2058.2.e.j 6
2058.2.e.k 6
2058.2.e.l 6
2058.2.e.m 12
2058.2.e.n 12
2058.2.f \(\chi_{2058}(1391, \cdot)\) n/a 192 2
2058.2.i \(\chi_{2058}(295, \cdot)\) n/a 288 6
2058.2.j \(\chi_{2058}(293, \cdot)\) n/a 552 6
2058.2.m \(\chi_{2058}(67, \cdot)\) n/a 552 12
2058.2.p \(\chi_{2058}(215, \cdot)\) n/a 1128 12
2058.2.q \(\chi_{2058}(43, \cdot)\) n/a 2688 42
2058.2.s \(\chi_{2058}(41, \cdot)\) n/a 5544 42
2058.2.u \(\chi_{2058}(25, \cdot)\) n/a 5544 84
2058.2.x \(\chi_{2058}(5, \cdot)\) n/a 10920 84

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2058))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2058)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(343))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(686))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1029))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2058))\)\(^{\oplus 1}\)