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Properties

Label 1368.3.i
Level $1368$
Weight $3$
Character orbit 1368.i
Rep. character $\chi_{1368}(37,\cdot)$
Character field $\Q$
Dimension $198$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1368.i (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1368, [\chi])\).

Total New Old
Modular forms 488 202 286
Cusp forms 472 198 274
Eisenstein series 16 4 12

Trace form

\( 198 q - 6 q^{4} - 4 q^{7} + O(q^{10}) \) \( 198 q - 6 q^{4} - 4 q^{7} - 30 q^{16} + 4 q^{17} + 44 q^{20} + 4 q^{23} - 954 q^{25} + 94 q^{26} - 118 q^{28} + 114 q^{38} + 116 q^{44} - 188 q^{47} + 1266 q^{49} + 96 q^{55} - 14 q^{58} - 368 q^{62} + 162 q^{64} - 58 q^{68} - 164 q^{73} - 52 q^{74} + 24 q^{76} + 416 q^{80} + 104 q^{82} - 422 q^{92} - 400 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1368, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1368, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1368, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)