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Properties

Label 845.6.u
Level $845$
Weight $6$
Character orbit 845.u
Rep. character $\chi_{845}(66,\cdot)$
Character field $\Q(\zeta_{13})$
Dimension $3624$
Sturm bound $546$

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Defining parameters

Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 845.u (of order \(13\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{13})\)
Sturm bound: \(546\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(845, [\chi])\).

Total New Old
Modular forms 5472 3624 1848
Cusp forms 5424 3624 1800
Eisenstein series 48 0 48

Trace form

\( 3624 q - 36 q^{3} - 4768 q^{4} - 228 q^{6} - 188 q^{7} + 852 q^{8} - 24358 q^{9} + O(q^{10}) \) \( 3624 q - 36 q^{3} - 4768 q^{4} - 228 q^{6} - 188 q^{7} + 852 q^{8} - 24358 q^{9} - 200 q^{10} + 4 q^{11} - 156 q^{12} + 2002 q^{13} - 360 q^{14} + 1100 q^{15} - 73480 q^{16} - 868 q^{17} + 3230 q^{18} - 2976 q^{19} + 3800 q^{20} + 10564 q^{21} + 13176 q^{22} + 75828 q^{23} + 31832 q^{24} - 188750 q^{25} - 572 q^{26} - 11988 q^{27} - 1596 q^{28} - 3088 q^{29} + 8000 q^{30} + 36968 q^{31} - 251142 q^{32} + 27548 q^{33} + 75794 q^{34} - 12700 q^{35} - 388460 q^{36} - 29092 q^{37} - 179170 q^{38} + 1144 q^{39} - 9600 q^{40} - 25456 q^{41} + 44312 q^{42} + 8456 q^{43} + 73476 q^{44} + 5800 q^{45} - 6892 q^{46} - 125478 q^{47} + 381858 q^{48} - 896456 q^{49} + 74036 q^{51} - 413998 q^{52} - 62088 q^{53} - 520492 q^{54} + 3600 q^{55} + 27140 q^{56} - 138882 q^{57} - 214492 q^{58} + 162480 q^{59} + 70400 q^{60} - 155356 q^{61} - 617898 q^{62} - 36500 q^{63} - 998204 q^{64} + 9750 q^{65} - 1247796 q^{66} - 585452 q^{67} - 309758 q^{68} - 19076 q^{69} - 66200 q^{70} + 509854 q^{71} - 79822 q^{72} + 169420 q^{73} - 132340 q^{74} - 22500 q^{75} - 2150088 q^{76} - 51844 q^{77} + 983944 q^{78} + 3444 q^{79} + 56800 q^{80} - 2213718 q^{81} + 472444 q^{82} - 151276 q^{83} + 309492 q^{84} - 17700 q^{85} - 2352 q^{86} - 81676 q^{87} - 16508 q^{88} + 1463568 q^{89} - 152100 q^{90} - 118196 q^{91} - 75244 q^{92} + 2614758 q^{93} + 1696580 q^{94} - 128800 q^{95} - 3829418 q^{96} - 150464 q^{97} - 110280 q^{98} - 393048 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(845, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(845, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(845, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)