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Properties

Label 1617.4.ck
Level $1617$
Weight $4$
Character orbit 1617.ck
Rep. character $\chi_{1617}(40,\cdot)$
Character field $\Q(\zeta_{210})$
Dimension $16128$
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.ck (of order \(210\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{210})\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 32448 16128 16320
Cusp forms 32064 16128 15936
Eisenstein series 384 0 384

Trace form

\( 16128 q + 1344 q^{4} + 48 q^{5} + 20 q^{7} + 3024 q^{9} + O(q^{10}) \) \( 16128 q + 1344 q^{4} + 48 q^{5} + 20 q^{7} + 3024 q^{9} + 196 q^{11} + 312 q^{14} + 630 q^{15} - 5320 q^{16} + 2180 q^{17} - 1792 q^{20} + 1540 q^{22} - 112 q^{23} + 1800 q^{24} + 8876 q^{25} + 1216 q^{26} + 360 q^{28} - 1400 q^{29} + 1242 q^{31} - 54 q^{33} + 10528 q^{34} + 2320 q^{35} + 24192 q^{36} + 252 q^{37} - 5456 q^{38} - 7920 q^{40} - 144 q^{42} - 2576 q^{44} - 1584 q^{45} + 3740 q^{47} + 3956 q^{49} + 10920 q^{51} - 2632 q^{53} - 546 q^{55} + 5248 q^{56} - 4200 q^{58} - 5608 q^{59} - 13104 q^{60} - 4920 q^{61} - 37520 q^{62} + 180 q^{63} - 47264 q^{64} + 2052 q^{66} - 2240 q^{67} + 720 q^{68} - 2904 q^{70} - 1120 q^{71} - 7680 q^{73} + 2800 q^{74} - 936 q^{75} + 5928 q^{77} - 3528 q^{78} + 2100 q^{79} + 10560 q^{80} - 27216 q^{81} + 9576 q^{82} - 4500 q^{84} - 1680 q^{85} + 1162 q^{86} - 27384 q^{88} + 3920 q^{89} + 3700 q^{91} - 7868 q^{92} + 672 q^{93} + 11340 q^{94} - 2660 q^{95} + O(q^{100}) \)

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

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