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Properties

Label 1682.4
Level 1682
Weight 4
Dimension 88095
Nonzero newspaces 8
Sturm bound 706440
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1682 = 2 \cdot 29^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(706440\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1682))\).

Total New Old
Modular forms 266119 88095 178024
Cusp forms 263711 88095 175616
Eisenstein series 2408 0 2408

Trace form

\( 88095 q + O(q^{10}) \) \( 88095 q - 616 q^{20} - 3136 q^{21} - 784 q^{22} - 112 q^{23} + 448 q^{24} + 1792 q^{25} + 1540 q^{26} + 4368 q^{27} + 1568 q^{29} + 4368 q^{30} + 2464 q^{31} + 1344 q^{33} - 140 q^{34} - 1568 q^{35} - 1568 q^{36} - 2464 q^{37} - 3472 q^{38} - 9184 q^{39} - 1456 q^{40} - 6930 q^{45} - 2968 q^{47} - 1680 q^{49} + 1680 q^{51} + 4662 q^{53} + 11424 q^{55} + 6384 q^{57} + 3080 q^{59} + 5040 q^{61} + 6048 q^{63} + 126 q^{65} - 3696 q^{67} - 8400 q^{69} - 10416 q^{70} - 32872 q^{71} - 23562 q^{73} - 11760 q^{74} - 12880 q^{75} - 2688 q^{76} - 1120 q^{77} + 3136 q^{78} + 3360 q^{79} + 25088 q^{81} + 7392 q^{82} + 16576 q^{83} + 13440 q^{84} + 28224 q^{85} + 24080 q^{86} + 12040 q^{87} + 22400 q^{89} + 20720 q^{90} + 22176 q^{91} + 9408 q^{92} + 9856 q^{93} + 3360 q^{94} + 6272 q^{95} - 5866 q^{97} - 10304 q^{98} - 37184 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1682))\)

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
1682.4.a \(\chi_{1682}(1, \cdot)\) 1682.4.a.a 1 1
1682.4.a.b 1
1682.4.a.c 2
1682.4.a.d 3
1682.4.a.e 3
1682.4.a.f 3
1682.4.a.g 4
1682.4.a.h 4
1682.4.a.i 4
1682.4.a.j 4
1682.4.a.k 6
1682.4.a.l 6
1682.4.a.m 8
1682.4.a.n 8
1682.4.a.o 9
1682.4.a.p 9
1682.4.a.q 12
1682.4.a.r 12
1682.4.a.s 12
1682.4.a.t 12
1682.4.a.u 16
1682.4.a.v 16
1682.4.a.w 24
1682.4.a.x 24
1682.4.b \(\chi_{1682}(1681, \cdot)\) n/a 202 1
1682.4.d \(\chi_{1682}(571, \cdot)\) n/a 1218 6
1682.4.e \(\chi_{1682}(63, \cdot)\) n/a 1212 6
1682.4.g \(\chi_{1682}(59, \cdot)\) n/a 6076 28
1682.4.h \(\chi_{1682}(57, \cdot)\) n/a 6104 28
1682.4.j \(\chi_{1682}(7, \cdot)\) n/a 36456 168
1682.4.k \(\chi_{1682}(5, \cdot)\) n/a 36624 168

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1682))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1682)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(841))\)\(^{\oplus 2}\)