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Properties

Label 2672.2.j
Level $2672$
Weight $2$
Character orbit 2672.j
Rep. character $\chi_{2672}(669,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $664$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 2672 = 2^{4} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2672.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2672, [\chi])\).

Total New Old
Modular forms 676 664 12
Cusp forms 668 664 4
Eisenstein series 8 0 8

Trace form

\( 664 q - 4 q^{4} - 12 q^{8} + O(q^{10}) \) \( 664 q - 4 q^{4} - 12 q^{8} - 12 q^{10} - 8 q^{11} - 4 q^{14} + 20 q^{16} - 20 q^{22} + 20 q^{24} - 24 q^{28} - 16 q^{29} + 24 q^{31} + 20 q^{34} + 24 q^{35} - 16 q^{37} + 20 q^{42} + 8 q^{43} + 26 q^{44} + 32 q^{46} - 40 q^{47} + 52 q^{48} - 664 q^{49} + 36 q^{50} - 40 q^{51} + 20 q^{52} + 16 q^{53} - 34 q^{54} - 48 q^{58} - 8 q^{60} - 58 q^{62} + 40 q^{63} + 32 q^{64} - 16 q^{65} - 12 q^{66} + 16 q^{67} - 52 q^{68} + 24 q^{70} + 40 q^{72} + 8 q^{74} - 60 q^{76} + 16 q^{77} - 8 q^{80} - 664 q^{81} + 40 q^{82} + 40 q^{83} + 110 q^{84} + 52 q^{86} - 40 q^{88} + 80 q^{90} + 48 q^{91} + 84 q^{92} - 8 q^{94} - 48 q^{95} - 4 q^{96} + 72 q^{98} - 40 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2672, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2672, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2672, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)