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Properties

Label 425.4.bg
Level $425$
Weight $4$
Character orbit 425.bg
Rep. character $\chi_{425}(12,\cdot)$
Character field $\Q(\zeta_{80})$
Dimension $4256$
Sturm bound $180$

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Defining parameters

Level: \( N \) \(=\) \( 425 = 5^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 425.bg (of order \(80\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 425 \)
Character field: \(\Q(\zeta_{80})\)
Sturm bound: \(180\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(425, [\chi])\).

Total New Old
Modular forms 4384 4384 0
Cusp forms 4256 4256 0
Eisenstein series 128 128 0

Trace form

\( 4256 q - 32 q^{2} - 32 q^{3} - 40 q^{4} - 32 q^{5} - 24 q^{6} - 32 q^{7} + 32 q^{8} - 40 q^{9} + O(q^{10}) \) \( 4256 q - 32 q^{2} - 32 q^{3} - 40 q^{4} - 32 q^{5} - 24 q^{6} - 32 q^{7} + 32 q^{8} - 40 q^{9} - 16 q^{10} - 24 q^{11} - 248 q^{12} - 24 q^{13} - 40 q^{14} + 304 q^{15} - 32 q^{17} - 64 q^{18} - 40 q^{19} - 2592 q^{20} - 24 q^{21} - 32 q^{22} - 32 q^{23} - 480 q^{25} - 64 q^{26} - 1136 q^{27} - 2336 q^{28} - 40 q^{29} - 5408 q^{30} - 24 q^{31} - 608 q^{32} + 768 q^{33} - 40 q^{34} - 64 q^{35} - 24 q^{36} - 896 q^{37} - 40 q^{38} + 392 q^{39} - 1768 q^{40} - 944 q^{41} - 1024 q^{42} - 32 q^{43} - 40 q^{44} - 32 q^{45} + 8616 q^{46} + 7560 q^{47} + 5152 q^{48} - 448 q^{50} - 64 q^{51} + 3008 q^{52} - 3080 q^{53} - 40 q^{54} - 2880 q^{55} - 24 q^{56} + 1824 q^{57} + 5120 q^{58} - 40 q^{59} - 5472 q^{60} - 24 q^{61} + 15712 q^{62} + 4264 q^{63} - 40 q^{64} + 968 q^{65} + 24576 q^{66} - 192 q^{67} + 11752 q^{68} - 80 q^{69} - 2336 q^{70} - 24 q^{71} + 10152 q^{72} - 1856 q^{73} + 4880 q^{74} - 5664 q^{75} - 64 q^{76} + 4912 q^{77} - 5464 q^{78} - 8680 q^{79} - 8880 q^{80} - 24 q^{81} - 6304 q^{82} + 20144 q^{83} - 22976 q^{85} - 48 q^{86} - 496 q^{87} - 8896 q^{88} - 40 q^{89} - 11888 q^{90} + 13696 q^{91} - 6224 q^{92} + 19904 q^{93} - 168 q^{94} + 11344 q^{95} - 3480 q^{96} + 4576 q^{97} + 7032 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(425, [\chi])\) into newform subspaces

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