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Properties

Label 2678.2.bw
Level $2678$
Weight $2$
Character orbit 2678.bw
Rep. character $\chi_{2678}(121,\cdot)$
Character field $\Q(\zeta_{102})$
Dimension $3904$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 2678 = 2 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2678.bw (of order \(102\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1339 \)
Character field: \(\Q(\zeta_{102})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 11776 3904 7872
Cusp forms 11520 3904 7616
Eisenstein series 256 0 256

Trace form

\( 3904 q - 2 q^{3} + 244 q^{4} + 132 q^{9} + O(q^{10}) \) \( 3904 q - 2 q^{3} + 244 q^{4} + 132 q^{9} + 4 q^{10} + 2 q^{12} - 6 q^{13} + 4 q^{14} - 36 q^{15} - 244 q^{16} - 4 q^{17} + 42 q^{19} - 6 q^{21} - 4 q^{22} - 122 q^{25} - 6 q^{26} + 16 q^{27} - 8 q^{29} - 6 q^{35} - 64 q^{36} + 30 q^{37} - 2 q^{38} + 142 q^{39} - 4 q^{40} - 8 q^{42} + 18 q^{43} + 12 q^{46} + 6 q^{47} - 2 q^{48} + 284 q^{49} + 36 q^{51} + 6 q^{52} - 2 q^{53} + 12 q^{55} - 4 q^{56} + 12 q^{57} - 6 q^{59} + 36 q^{60} + 2 q^{61} - 20 q^{62} - 42 q^{63} + 244 q^{64} + 28 q^{65} - 152 q^{66} + 42 q^{67} + 4 q^{68} - 232 q^{69} - 24 q^{70} - 2 q^{74} - 20 q^{75} - 42 q^{76} + 130 q^{77} + 4 q^{78} + 44 q^{79} + 146 q^{81} - 8 q^{82} - 30 q^{83} - 232 q^{84} - 120 q^{85} + 54 q^{86} - 24 q^{87} + 4 q^{88} - 36 q^{89} - 36 q^{90} + 228 q^{91} - 74 q^{94} - 28 q^{95} + 64 q^{97} - 408 q^{98} - 60 q^{99} + O(q^{100}) \)

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

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