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Properties

Label 1617.4.n
Level $1617$
Weight $4$
Character orbit 1617.n
Rep. character $\chi_{1617}(815,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $800$
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.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 1376 800 576
Cusp forms 1312 800 512
Eisenstein series 64 0 64

Trace form

\( 800 q + 1600 q^{4} + 28 q^{9} + O(q^{10}) \) \( 800 q + 1600 q^{4} + 28 q^{9} - 330 q^{12} - 184 q^{15} - 6400 q^{16} + 38 q^{18} + 612 q^{19} + 288 q^{24} - 10000 q^{25} - 2152 q^{30} - 1020 q^{31} + 2252 q^{36} + 224 q^{37} - 556 q^{39} + 2340 q^{40} + 968 q^{43} + 3348 q^{45} - 108 q^{46} - 2088 q^{51} - 4272 q^{52} - 3810 q^{54} - 2720 q^{57} + 2640 q^{58} - 3208 q^{60} + 4728 q^{61} - 53072 q^{64} + 1650 q^{66} - 788 q^{67} - 8032 q^{72} - 3492 q^{73} + 792 q^{75} + 5544 q^{78} - 1484 q^{79} - 436 q^{81} + 4788 q^{82} - 1344 q^{85} - 3636 q^{87} + 792 q^{88} - 2992 q^{93} - 288 q^{94} - 7002 q^{96} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1617, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)