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Properties

Label 1617.4.be
Level $1617$
Weight $4$
Character orbit 1617.be
Rep. character $\chi_{1617}(76,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $2016$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1617.be (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1617, [\chi])\).

Total New Old
Modular forms 4056 2016 2040
Cusp forms 4008 2016 1992
Eisenstein series 48 0 48

Trace form

\( 2016 q + 1344 q^{4} + 3024 q^{9} + O(q^{10}) \) \( 2016 q + 1344 q^{4} + 3024 q^{9} + 196 q^{11} - 40 q^{14} - 420 q^{15} - 5488 q^{16} - 1792 q^{20} + 280 q^{22} + 224 q^{23} + 7448 q^{25} + 2128 q^{26} - 2632 q^{34} - 12096 q^{36} - 504 q^{37} + 3472 q^{38} - 732 q^{42} + 2576 q^{44} + 1008 q^{45} - 1456 q^{47} - 2272 q^{49} + 2912 q^{53} - 294 q^{55} - 376 q^{56} + 1680 q^{58} - 7672 q^{59} + 5040 q^{60} + 24808 q^{64} - 1120 q^{67} + 7716 q^{70} - 1120 q^{71} - 768 q^{77} - 3528 q^{78} - 27216 q^{81} - 3948 q^{86} + 8568 q^{88} + 560 q^{89} - 15712 q^{91} - 4116 q^{92} - 1344 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1617, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1617, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1617, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 2}\)