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Properties

Label 350.10.h
Level $350$
Weight $10$
Character orbit 350.h
Rep. character $\chi_{350}(71,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $536$
Sturm bound $600$

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Defining parameters

Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 350.h (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(350, [\chi])\).

Total New Old
Modular forms 2176 536 1640
Cusp forms 2144 536 1608
Eisenstein series 32 0 32

Trace form

\( 536 q + 32 q^{2} - 592 q^{3} - 34304 q^{4} - 14294 q^{5} + 8192 q^{8} - 933442 q^{9} + O(q^{10}) \) \( 536 q + 32 q^{2} - 592 q^{3} - 34304 q^{4} - 14294 q^{5} + 8192 q^{8} - 933442 q^{9} - 43424 q^{10} + 58564 q^{11} + 227328 q^{12} + 246428 q^{13} + 153664 q^{14} - 120500 q^{15} - 8781824 q^{16} + 452884 q^{17} - 4475392 q^{18} - 2698704 q^{19} + 2410496 q^{20} + 777924 q^{21} + 1021248 q^{22} + 587104 q^{23} - 29188846 q^{25} + 3609792 q^{26} + 17127152 q^{27} + 3551352 q^{29} - 6080000 q^{30} - 12356496 q^{31} - 8388608 q^{32} - 3213352 q^{33} + 34989600 q^{34} + 6204184 q^{35} - 238961152 q^{36} + 22772094 q^{37} - 7879296 q^{38} + 22266708 q^{39} - 11116544 q^{40} + 33498012 q^{41} - 56996656 q^{43} + 14992384 q^{44} - 79788458 q^{45} + 5322176 q^{46} + 11596184 q^{47} + 58195968 q^{48} + 3089933336 q^{49} - 45066016 q^{50} - 504513392 q^{51} + 63085568 q^{52} + 48277274 q^{53} + 250537344 q^{54} + 345416464 q^{55} + 39337984 q^{56} - 277068912 q^{57} - 159923008 q^{58} - 927270168 q^{59} + 231577600 q^{60} + 859765732 q^{61} + 22855936 q^{62} + 383747028 q^{63} - 2248146944 q^{64} - 1654223566 q^{65} + 1115210008 q^{67} + 115938304 q^{68} - 1602712936 q^{69} - 153510336 q^{70} - 1067773288 q^{71} + 197992448 q^{72} - 1089698212 q^{73} - 2675329088 q^{74} + 1785220200 q^{75} + 460578816 q^{76} + 783916896 q^{77} + 1377583232 q^{78} + 1096387760 q^{79} + 106561536 q^{80} - 4727790626 q^{81} + 2467420992 q^{82} - 2215432352 q^{83} + 199148544 q^{84} - 5744781958 q^{85} + 1094016320 q^{86} - 7557252204 q^{87} - 174292992 q^{88} - 217580714 q^{89} - 2369895968 q^{90} + 274299844 q^{91} - 650269696 q^{92} - 12445741888 q^{93} + 3468206280 q^{95} - 4061897644 q^{97} + 184473632 q^{98} - 4132160216 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(350, [\chi])\) into newform subspaces

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

Decomposition of \(S_{10}^{\mathrm{old}}(350, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(350, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)