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Properties

Label 841.4
Level 841
Weight 4
Dimension 87521
Nonzero newspaces 8
Sturm bound 235480
Trace bound 1

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Defining parameters

Level: \( N \) = \( 841 = 29^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(235480\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(841))\).

Total New Old
Modular forms 88907 88670 237
Cusp forms 87703 87521 182
Eisenstein series 1204 1149 55

Trace form

\( 87521 q - 378 q^{2} - 378 q^{3} - 378 q^{4} - 378 q^{5} - 378 q^{6} - 378 q^{7} - 378 q^{8} - 378 q^{9} + O(q^{10}) \) \( 87521 q - 378 q^{2} - 378 q^{3} - 378 q^{4} - 378 q^{5} - 378 q^{6} - 378 q^{7} - 378 q^{8} - 378 q^{9} - 378 q^{10} - 378 q^{11} - 378 q^{12} - 378 q^{13} - 378 q^{14} - 378 q^{15} - 378 q^{16} - 378 q^{17} - 378 q^{18} - 378 q^{19} + 1470 q^{20} + 1190 q^{21} + 406 q^{22} - 322 q^{23} - 1722 q^{24} - 1274 q^{25} - 1918 q^{26} - 2562 q^{27} - 3486 q^{28} - 1176 q^{29} - 5110 q^{30} - 1610 q^{31} - 2170 q^{32} - 1050 q^{33} - 238 q^{34} + 406 q^{35} + 4326 q^{36} + 854 q^{37} + 3094 q^{38} + 4214 q^{39} + 3990 q^{40} - 378 q^{41} - 378 q^{42} - 378 q^{43} + 3122 q^{44} + 6552 q^{45} + 10122 q^{46} + 2590 q^{47} + 7014 q^{48} + 1302 q^{49} - 574 q^{50} - 2058 q^{51} - 6426 q^{52} - 5040 q^{53} - 11718 q^{54} - 11802 q^{55} - 10934 q^{56} - 6734 q^{57} - 9968 q^{58} - 3822 q^{59} - 17290 q^{60} - 5418 q^{61} - 7630 q^{62} - 6426 q^{63} - 4158 q^{64} - 504 q^{65} + 2982 q^{66} + 3318 q^{67} + 10010 q^{68} + 8022 q^{69} + 32214 q^{70} + 19558 q^{71} + 41874 q^{72} + 17808 q^{73} + 17402 q^{74} + 6062 q^{75} + 4998 q^{76} + 182 q^{77} - 3514 q^{78} - 2058 q^{79} - 17626 q^{80} - 12922 q^{81} - 7770 q^{82} - 8666 q^{83} - 26502 q^{84} - 14490 q^{85} - 24430 q^{86} - 6412 q^{87} - 28966 q^{88} - 11578 q^{89} - 20342 q^{90} - 11466 q^{91} - 19194 q^{92} - 5306 q^{93} - 3738 q^{94} - 3514 q^{95} + 23450 q^{96} + 23212 q^{97} + 36666 q^{98} + 44590 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(841))\)

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
841.4.a \(\chi_{841}(1, \cdot)\) 841.4.a.a 2 1
841.4.a.b 5
841.4.a.c 6
841.4.a.d 7
841.4.a.e 7
841.4.a.f 14
841.4.a.g 14
841.4.a.h 21
841.4.a.i 21
841.4.a.j 28
841.4.a.k 28
841.4.a.l 36
841.4.b \(\chi_{841}(840, \cdot)\) n/a 190 1
841.4.d \(\chi_{841}(190, \cdot)\) n/a 1134 6
841.4.e \(\chi_{841}(63, \cdot)\) n/a 1140 6
841.4.g \(\chi_{841}(30, \cdot)\) n/a 6076 28
841.4.h \(\chi_{841}(28, \cdot)\) n/a 6048 28
841.4.j \(\chi_{841}(7, \cdot)\) n/a 36456 168
841.4.k \(\chi_{841}(4, \cdot)\) n/a 36288 168

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(841))\) into lower level spaces

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