Properties

Label 2678.2.bo
Level $2678$
Weight $2$
Character orbit 2678.bo
Rep. character $\chi_{2678}(25,\cdot)$
Character field $\Q(\zeta_{102})$
Dimension $3840$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 2678 = 2 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2678.bo (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 3840 7936
Cusp forms 11520 3840 7680
Eisenstein series 256 0 256

Trace form

\( 3840q - 120q^{4} - 200q^{9} + O(q^{10}) \) \( 3840q - 120q^{4} - 200q^{9} - 8q^{10} - 4q^{13} - 8q^{14} + 120q^{16} - 4q^{17} + 8q^{22} - 120q^{25} + 6q^{26} - 8q^{29} - 12q^{35} - 236q^{36} + 4q^{38} - 76q^{39} - 4q^{40} + 16q^{42} - 16q^{43} - 96q^{49} - 2q^{52} - 20q^{53} + 36q^{55} - 4q^{56} - 48q^{61} + 28q^{62} + 240q^{64} - 8q^{65} - 56q^{66} + 4q^{68} + 152q^{69} - 8q^{74} + 8q^{75} - 212q^{77} - 2q^{78} + 48q^{79} - 96q^{81} + 4q^{82} + 36q^{87} + 4q^{88} - 96q^{90} - 222q^{91} + 160q^{94} - 40q^{95} + O(q^{100}) \)

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

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