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Properties

Label 1421.4.cp
Level $1421$
Weight $4$
Character orbit 1421.cp
Rep. character $\chi_{1421}(153,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $5016$
Sturm bound $560$

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Defining parameters

Level: \( N \) \(=\) \( 1421 = 7^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1421.cp (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1421 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(560\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1421, [\chi])\).

Total New Old
Modular forms 5064 5064 0
Cusp forms 5016 5016 0
Eisenstein series 48 48 0

Trace form

\( 5016 q - 10 q^{2} - 14 q^{3} - 14 q^{4} - 28 q^{5} - 28 q^{6} - 10 q^{7} - 42 q^{8} - 14 q^{9} + O(q^{10}) \) \( 5016 q - 10 q^{2} - 14 q^{3} - 14 q^{4} - 28 q^{5} - 28 q^{6} - 10 q^{7} - 42 q^{8} - 14 q^{9} - 126 q^{10} - 10 q^{11} - 126 q^{12} - 14 q^{13} + 180 q^{14} - 658 q^{15} + 13178 q^{16} + 322 q^{17} - 326 q^{18} - 910 q^{20} + 1006 q^{21} - 14 q^{22} - 6 q^{23} - 910 q^{24} + 122980 q^{25} - 14 q^{26} + 910 q^{27} + 46 q^{29} - 3892 q^{30} - 584 q^{32} - 14 q^{33} - 14 q^{34} - 1764 q^{35} + 180876 q^{36} - 1186 q^{37} + 952 q^{38} + 938 q^{39} - 14 q^{40} - 2898 q^{41} - 3038 q^{42} - 122 q^{43} + 1354 q^{44} - 1764 q^{45} + 330 q^{46} - 98 q^{47} - 3024 q^{48} + 3450 q^{49} + 970 q^{50} - 5810 q^{52} + 5874 q^{53} - 7014 q^{54} - 12516 q^{55} + 6444 q^{56} + 3920 q^{57} + 3350 q^{58} + 1736 q^{59} - 6664 q^{60} + 238 q^{61} - 714 q^{62} + 4438 q^{63} - 14 q^{64} + 252 q^{65} - 3038 q^{66} - 28 q^{67} - 7238 q^{68} - 14 q^{69} - 2898 q^{70} - 11970 q^{71} - 6552 q^{72} - 14 q^{73} - 3366 q^{74} - 10430 q^{75} - 14 q^{76} - 7156 q^{77} + 1330 q^{78} + 648 q^{79} - 2646 q^{80} + 74078 q^{81} - 14 q^{82} + 4066 q^{84} - 4396 q^{85} - 14 q^{87} + 5712 q^{88} - 5474 q^{89} - 5166 q^{90} + 5208 q^{91} - 9422 q^{92} - 14 q^{93} - 1918 q^{94} + 3332 q^{95} - 910 q^{96} - 8904 q^{97} - 17394 q^{98} - 3112 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1421, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.