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Properties

Label 2366.4.v
Level $2366$
Weight $4$
Character orbit 2366.v
Rep. character $\chi_{2366}(361,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $616$
Sturm bound $1456$

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Defining parameters

Level: \( N \) \(=\) \( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2366.v (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1456\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2366, [\chi])\).

Total New Old
Modular forms 2240 616 1624
Cusp forms 2128 616 1512
Eisenstein series 112 0 112

Trace form

\( 616 q + 1232 q^{4} + 36 q^{7} + 5608 q^{9} + O(q^{10}) \) \( 616 q + 1232 q^{4} + 36 q^{7} + 5608 q^{9} + 80 q^{10} - 36 q^{14} + 120 q^{15} - 4928 q^{16} - 140 q^{17} - 192 q^{18} + 168 q^{21} - 56 q^{22} + 228 q^{23} + 7828 q^{25} - 552 q^{27} + 216 q^{28} - 380 q^{29} + 608 q^{30} + 300 q^{31} - 452 q^{35} + 11216 q^{36} - 336 q^{37} - 208 q^{38} + 160 q^{40} + 288 q^{41} + 652 q^{42} - 404 q^{43} - 168 q^{44} + 240 q^{45} + 360 q^{46} + 270 q^{47} + 1746 q^{49} - 2232 q^{50} + 972 q^{51} + 528 q^{53} + 180 q^{54} + 636 q^{55} - 336 q^{56} + 480 q^{60} - 4312 q^{61} - 1428 q^{62} + 2160 q^{63} - 39424 q^{64} + 416 q^{66} + 560 q^{68} - 1268 q^{69} + 2880 q^{70} + 1296 q^{71} + 2346 q^{73} - 264 q^{74} - 7568 q^{75} - 504 q^{76} - 1324 q^{77} - 514 q^{79} + 49912 q^{81} + 1600 q^{82} + 552 q^{84} + 1560 q^{85} - 948 q^{86} - 1956 q^{87} - 448 q^{88} + 7476 q^{89} - 384 q^{90} + 1824 q^{92} + 3258 q^{93} + 488 q^{94} - 1908 q^{95} + 5118 q^{97} + 408 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2366, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2366, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2366, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1183, [\chi])\)\(^{\oplus 2}\)