↑

Properties

Label 2678.2.bj
Level $2678$
Weight $2$
Character orbit 2678.bj
Rep. character $\chi_{2678}(9,\cdot)$
Character field $\Q(\zeta_{51})$
Dimension $3840$
Sturm bound $728$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2678 = 2 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2678.bj (of order \(51\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1339 \)
Character field: \(\Q(\zeta_{51})\)
Sturm bound: \(728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2678, [\chi])\).

Total New Old
Modular forms 11776 3840 7936
Cusp forms 11520 3840 7680
Eisenstein series 256 0 256

Trace form

\( 3840 q + 120 q^{4} + 8 q^{7} + 108 q^{9} + O(q^{10}) \) \( 3840 q + 120 q^{4} + 8 q^{7} + 108 q^{9} + 4 q^{10} + 8 q^{11} - 20 q^{13} + 8 q^{14} - 16 q^{15} + 120 q^{16} - 4 q^{17} + 32 q^{21} + 4 q^{22} - 8 q^{23} - 208 q^{25} - 4 q^{26} + 8 q^{28} - 8 q^{29} - 32 q^{31} - 8 q^{33} + 4 q^{35} + 176 q^{36} - 12 q^{37} + 8 q^{38} - 36 q^{39} - 8 q^{40} + 16 q^{41} + 8 q^{42} - 24 q^{43} - 16 q^{44} - 8 q^{47} + 108 q^{49} - 16 q^{51} + 16 q^{52} - 16 q^{53} + 24 q^{54} - 4 q^{55} - 4 q^{56} + 40 q^{57} + 12 q^{58} - 8 q^{59} + 32 q^{60} + 4 q^{62} - 20 q^{63} - 240 q^{64} + 20 q^{65} + 272 q^{66} - 24 q^{67} - 4 q^{68} - 152 q^{69} + 32 q^{70} - 280 q^{71} - 56 q^{73} + 32 q^{74} - 48 q^{75} - 248 q^{77} + 16 q^{78} + 32 q^{79} + 72 q^{81} + 8 q^{82} - 40 q^{83} + 52 q^{84} + 4 q^{85} - 28 q^{86} - 16 q^{87} + 4 q^{88} - 20 q^{89} - 32 q^{90} + 12 q^{91} + 16 q^{92} + 176 q^{93} - 80 q^{94} - 8 q^{95} - 234 q^{97} + 152 q^{98} - 284 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2678, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2678, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2678, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1339, [\chi])\)\(^{\oplus 2}\)