Properties

Label 2366.2.bo
Level $2366$
Weight $2$
Character orbit 2366.bo
Rep. character $\chi_{2366}(121,\cdot)$
Character field $\Q(\zeta_{78})$
Dimension $2928$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2366.bo (of order \(78\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1183 \)
Character field: \(\Q(\zeta_{78})\)
Sturm bound: \(728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2366, [\chi])\).

Total New Old
Modular forms 8832 2928 5904
Cusp forms 8640 2928 5712
Eisenstein series 192 0 192

Trace form

\( 2928q + 4q^{3} - 122q^{4} + 2q^{7} - 256q^{9} + O(q^{10}) \) \( 2928q + 4q^{3} - 122q^{4} + 2q^{7} - 256q^{9} - 8q^{10} + 2q^{12} + 72q^{13} + 2q^{14} + 64q^{15} + 122q^{16} + 8q^{17} + 24q^{18} - 14q^{21} + 4q^{23} - 126q^{25} + 6q^{26} + 16q^{27} + 4q^{28} - 4q^{29} - 44q^{30} - 6q^{31} + 30q^{35} - 128q^{36} + 36q^{37} + 12q^{38} - 26q^{39} - 4q^{40} - 18q^{41} - 2q^{42} - 4q^{43} + 6q^{44} + 60q^{45} - 12q^{46} + 18q^{47} - 2q^{48} + 30q^{49} + 12q^{50} + 8q^{51} - 206q^{53} - 60q^{54} + 6q^{55} - 2q^{56} - 104q^{58} + 12q^{60} + 20q^{61} + 22q^{62} + 196q^{63} + 244q^{64} + 18q^{65} - 32q^{66} - 156q^{67} - 8q^{68} + 26q^{69} + 264q^{70} + 174q^{71} - 72q^{73} + 196q^{74} - 584q^{75} - 50q^{76} - 22q^{77} - 20q^{78} - 38q^{79} - 260q^{81} - 32q^{82} - 16q^{84} - 92q^{85} - 114q^{86} + 32q^{87} + 18q^{89} - 40q^{90} - 8q^{91} + 8q^{92} + 278q^{93} + 28q^{94} + 108q^{95} - 12q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2366, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2366, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2366, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1183, [\chi])\)\(^{\oplus 2}\)