Properties

Label 2678.2.cd
Level $2678$
Weight $2$
Character orbit 2678.cd
Rep. character $\chi_{2678}(11,\cdot)$
Character field $\Q(\zeta_{204})$
Dimension $7808$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 2678 = 2 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2678.cd (of order \(204\) and degree \(64\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1339 \)
Character field: \(\Q(\zeta_{204})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 23552 7808 15744
Cusp forms 23040 7808 15232
Eisenstein series 512 0 512

Trace form

\( 7808 q - 12 q^{7} - 248 q^{9} + O(q^{10}) \) \( 7808 q - 12 q^{7} - 248 q^{9} - 12 q^{11} + 4 q^{12} + 36 q^{13} + 40 q^{15} + 488 q^{16} - 52 q^{19} - 8 q^{21} - 24 q^{23} - 24 q^{25} - 16 q^{26} - 12 q^{28} - 16 q^{29} - 8 q^{31} + 8 q^{33} + 12 q^{35} + 360 q^{36} - 4 q^{37} + 220 q^{39} + 16 q^{41} + 44 q^{43} - 36 q^{44} + 12 q^{46} - 12 q^{47} - 24 q^{51} - 24 q^{52} + 36 q^{53} - 32 q^{55} + 32 q^{57} + 36 q^{58} - 28 q^{59} + 32 q^{60} - 104 q^{63} - 240 q^{66} - 20 q^{67} - 120 q^{69} + 48 q^{70} + 472 q^{71} - 4 q^{73} - 12 q^{74} - 64 q^{75} - 32 q^{76} + 816 q^{77} + 24 q^{78} + 16 q^{79} + 276 q^{81} + 32 q^{83} + 200 q^{84} + 88 q^{85} - 68 q^{86} + 24 q^{87} + 12 q^{89} + 8 q^{91} - 8 q^{92} - 368 q^{93} - 76 q^{94} + 336 q^{97} + 352 q^{98} - 448 q^{99} + O(q^{100}) \)

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

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