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Properties

Label 207.8.i
Level $207$
Weight $8$
Character orbit 207.i
Rep. character $\chi_{207}(55,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $690$
Sturm bound $192$

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Defining parameters

Level: \( N \) \(=\) \( 207 = 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 207.i (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 \(M_{8}(207, [\chi])\).

Total New Old
Modular forms 1720 710 1010
Cusp forms 1640 690 950
Eisenstein series 80 20 60

Trace form

\( 690 q + 23 q^{2} - 4595 q^{4} + 403 q^{5} - 301 q^{7} - 328 q^{8} + O(q^{10}) \) \( 690 q + 23 q^{2} - 4595 q^{4} + 403 q^{5} - 301 q^{7} - 328 q^{8} + 4747 q^{10} + 4385 q^{11} + 9765 q^{13} + 46527 q^{14} - 164139 q^{16} - 8064 q^{17} - 174602 q^{19} - 7957 q^{20} + 378358 q^{22} + 148576 q^{23} - 1320232 q^{25} - 415848 q^{26} - 152653 q^{28} - 167020 q^{29} + 1088942 q^{31} + 1022367 q^{32} + 228717 q^{34} + 803741 q^{35} - 709967 q^{37} - 1085402 q^{38} - 2042429 q^{40} - 1358999 q^{41} - 742027 q^{43} + 5720840 q^{44} - 8380163 q^{46} + 1764330 q^{47} - 8298010 q^{49} - 8661284 q^{50} + 12553016 q^{52} - 4118029 q^{53} - 10175973 q^{55} + 2310842 q^{56} + 1313989 q^{58} + 1118913 q^{59} + 13421727 q^{61} + 8337920 q^{62} - 11913998 q^{64} - 9172570 q^{65} - 10678791 q^{67} - 48824242 q^{68} + 4842686 q^{70} - 6782334 q^{71} - 240985 q^{73} + 16486468 q^{74} + 32996266 q^{76} + 44771790 q^{77} + 11209905 q^{79} - 40678230 q^{80} - 62493134 q^{82} - 62214854 q^{83} - 28345059 q^{85} + 8036375 q^{86} + 47019865 q^{88} + 1467819 q^{89} + 66859948 q^{91} + 68842316 q^{92} + 18251155 q^{94} - 32338416 q^{95} - 9479966 q^{97} - 30978085 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(207, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(207, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(207, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)