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Properties

Label 350.4.m
Level $350$
Weight $4$
Character orbit 350.m
Rep. character $\chi_{350}(29,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $176$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 350.m (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(350, [\chi])\).

Total New Old
Modular forms 736 176 560
Cusp forms 704 176 528
Eisenstein series 32 0 32

Trace form

\( 176 q + 176 q^{4} + 76 q^{5} + 488 q^{9} + O(q^{10}) \) \( 176 q + 176 q^{4} + 76 q^{5} + 488 q^{9} + 56 q^{10} + 44 q^{11} - 160 q^{12} - 56 q^{14} - 260 q^{15} - 704 q^{16} - 144 q^{19} + 256 q^{20} + 84 q^{21} + 360 q^{22} + 440 q^{23} + 1764 q^{25} - 368 q^{26} + 1080 q^{27} - 28 q^{29} + 80 q^{30} + 144 q^{31} - 1920 q^{33} - 960 q^{34} - 56 q^{35} - 1952 q^{36} - 1360 q^{37} - 732 q^{39} - 224 q^{40} + 112 q^{41} - 176 q^{44} - 408 q^{45} + 1016 q^{46} - 2080 q^{47} - 640 q^{48} - 8624 q^{49} - 456 q^{50} - 592 q^{51} + 2260 q^{53} + 1104 q^{54} - 2896 q^{55} + 224 q^{56} - 2808 q^{59} - 2560 q^{60} - 1288 q^{61} - 2660 q^{63} + 2816 q^{64} - 3956 q^{65} + 7560 q^{67} - 1336 q^{69} + 504 q^{70} - 1048 q^{71} + 5760 q^{73} + 4752 q^{74} + 3360 q^{75} - 384 q^{76} - 1120 q^{77} + 13280 q^{78} + 3760 q^{79} - 64 q^{80} + 1864 q^{81} - 4920 q^{83} - 336 q^{84} - 4868 q^{85} + 1720 q^{86} - 18780 q^{87} + 1256 q^{89} - 3048 q^{90} + 364 q^{91} - 3600 q^{92} + 3200 q^{95} - 5280 q^{97} + 1544 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(350, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(350, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(350, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)