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Properties

Label 138.8.e
Level $138$
Weight $8$
Character orbit 138.e
Rep. character $\chi_{138}(13,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $280$
Sturm bound $192$

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Defining parameters

Level: \( N \) \(=\) \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 138.e (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Sturm bound: \(192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(138, [\chi])\).

Total New Old
Modular forms 1720 280 1440
Cusp forms 1640 280 1360
Eisenstein series 80 0 80

Trace form

\( 280 q - 1792 q^{4} + 8 q^{5} + 1576 q^{7} - 20412 q^{9} + O(q^{10}) \) \( 280 q - 1792 q^{4} + 8 q^{5} + 1576 q^{7} - 20412 q^{9} - 4000 q^{10} - 14664 q^{11} + 9168 q^{13} + 17984 q^{14} + 27432 q^{15} - 114688 q^{16} - 110900 q^{17} - 245968 q^{19} - 2304 q^{20} - 37044 q^{21} + 420096 q^{22} + 759968 q^{23} - 1053500 q^{25} - 879520 q^{26} - 453888 q^{28} + 546996 q^{29} + 49248 q^{30} + 1934884 q^{31} - 606204 q^{33} - 170176 q^{34} + 2666948 q^{35} - 1306368 q^{36} + 296768 q^{37} + 310016 q^{38} - 2273508 q^{39} - 256000 q^{40} - 2061876 q^{41} + 355104 q^{42} + 57328 q^{43} - 938496 q^{44} + 5832 q^{45} + 57760 q^{46} + 4405584 q^{47} - 2779596 q^{49} + 1611072 q^{50} - 5956848 q^{51} + 586752 q^{52} - 7658196 q^{53} + 11470456 q^{55} + 1150976 q^{56} + 10125216 q^{57} + 649184 q^{58} - 9607516 q^{59} + 1755648 q^{60} - 15271444 q^{61} - 2037440 q^{62} + 1148904 q^{63} - 7340032 q^{64} - 3061952 q^{65} - 3167424 q^{66} + 9863816 q^{67} - 4459008 q^{68} + 194940 q^{69} + 16478592 q^{70} - 9166200 q^{71} - 18240228 q^{73} + 4278464 q^{74} + 3296160 q^{75} + 221952 q^{76} + 29004928 q^{77} + 494208 q^{78} + 7093716 q^{79} + 32768 q^{80} - 14880348 q^{81} + 41957152 q^{82} - 19714780 q^{83} - 2370816 q^{84} - 55446128 q^{85} - 817088 q^{86} - 2467800 q^{87} - 3098624 q^{88} - 5068844 q^{89} - 2916000 q^{90} + 76979800 q^{91} - 2652672 q^{92} + 18233856 q^{93} - 4885824 q^{94} - 162208012 q^{95} - 28324964 q^{97} + 98295232 q^{98} + 51248700 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(138, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(138, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(138, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)