↑

Properties

Label 350.10.m
Level $350$
Weight $10$
Character orbit 350.m
Rep. character $\chi_{350}(29,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $544$
Sturm bound $600$

Related objects

Downloads

Learn more

Defining parameters

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

Dimensions

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

Total New Old
Modular forms 2176 544 1632
Cusp forms 2144 544 1600
Eisenstein series 32 0 32

Trace form

\( 544 q + 34816 q^{4} + 11896 q^{5} + 838028 q^{9} + O(q^{10}) \) \( 544 q + 34816 q^{4} + 11896 q^{5} + 838028 q^{9} + 58816 q^{10} - 58564 q^{11} - 378880 q^{12} + 153664 q^{14} + 201148 q^{15} - 8912896 q^{16} - 2698704 q^{19} - 45056 q^{20} - 777924 q^{21} + 1702080 q^{22} - 3318920 q^{23} + 3781320 q^{25} - 5514112 q^{26} + 29130840 q^{27} + 18180772 q^{29} - 8891392 q^{30} + 12356496 q^{31} + 18610560 q^{33} + 42040320 q^{34} - 6204184 q^{35} - 214535168 q^{36} - 52790180 q^{37} + 22266708 q^{39} - 15056896 q^{40} + 37278968 q^{41} + 14992384 q^{44} + 310353252 q^{45} - 5322176 q^{46} - 250818240 q^{47} - 96993280 q^{48} - 3136051744 q^{49} + 41379904 q^{50} + 504513392 q^{51} + 153543320 q^{53} + 250537344 q^{54} + 411454384 q^{55} - 39337984 q^{56} - 927270168 q^{59} + 210931712 q^{60} - 872974352 q^{61} + 639578380 q^{63} + 2281701376 q^{64} - 1350153696 q^{65} + 415552680 q^{67} + 731642744 q^{69} - 153510336 q^{70} + 985273608 q^{71} - 1966999680 q^{73} - 2009872768 q^{74} - 166553520 q^{75} - 460578816 q^{76} - 1306528160 q^{77} + 416140160 q^{78} + 1096387760 q^{79} - 263716864 q^{80} - 10255394924 q^{81} + 2510592360 q^{83} + 199148544 q^{84} - 3400387672 q^{85} - 1094016320 q^{86} - 6049924140 q^{87} - 2252009164 q^{89} - 808450368 q^{90} - 274299844 q^{91} + 1948953600 q^{92} - 2080197536 q^{95} + 1039932960 q^{97} - 9021082936 q^{99} + O(q^{100}) \)

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

\( S_{10}^{\mathrm{old}}(350, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)