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Properties

Label 1296.4.l
Level $1296$
Weight $4$
Character orbit 1296.l
Rep. character $\chi_{1296}(323,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $568$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 1296 = 2^{4} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1296.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1296, [\chi])\).

Total New Old
Modular forms 1320 584 736
Cusp forms 1272 568 704
Eisenstein series 48 16 32

Trace form

\( 568 q + 4 q^{4} + 8 q^{7} + O(q^{10}) \) \( 568 q + 4 q^{4} + 8 q^{7} - 8 q^{10} + 4 q^{13} - 356 q^{16} - 8 q^{19} + 4 q^{22} + 248 q^{28} - 28 q^{34} - 8 q^{37} + 4 q^{40} + 4 q^{43} + 32 q^{46} + 25488 q^{49} + 4 q^{52} - 16 q^{55} + 3856 q^{58} + 4 q^{61} + 532 q^{64} - 2444 q^{67} - 3592 q^{70} - 5900 q^{76} - 1380 q^{82} - 496 q^{85} + 652 q^{88} + 1364 q^{91} - 60 q^{94} + 8 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1296, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1296, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1296, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)