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Properties

Label 350.10.q
Level $350$
Weight $10$
Character orbit 350.q
Rep. character $\chi_{350}(11,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $1440$
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.q (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(600\)

Dimensions

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

Total New Old
Modular forms 4352 1440 2912
Cusp forms 4288 1440 2848
Eisenstein series 64 0 64

Trace form

\( 1440 q + 46080 q^{4} + 568 q^{5} - 10368 q^{6} - 2132 q^{7} + 1180980 q^{9} + O(q^{10}) \) \( 1440 q + 46080 q^{4} + 568 q^{5} - 10368 q^{6} - 2132 q^{7} + 1180980 q^{9} - 25632 q^{10} + 22596 q^{11} - 975652 q^{15} + 11796480 q^{16} + 2863776 q^{17} - 276352 q^{18} + 521284 q^{19} - 290816 q^{20} + 1288272 q^{21} - 5534208 q^{22} - 556138 q^{23} - 5308416 q^{24} - 1337566 q^{25} - 21934848 q^{26} + 46074696 q^{27} - 157184 q^{28} - 6884256 q^{29} - 182048 q^{30} - 10304874 q^{31} + 23996316 q^{33} - 21381376 q^{34} - 23059636 q^{35} - 604661760 q^{36} + 34038456 q^{37} + 17387392 q^{38} + 64905388 q^{39} - 6561792 q^{40} + 8174752 q^{41} - 65141984 q^{42} + 144791440 q^{43} - 3856384 q^{44} - 54624464 q^{45} - 30497472 q^{46} + 931400 q^{47} - 101073276 q^{49} + 23070720 q^{50} - 87170412 q^{51} - 55353656 q^{53} + 136048896 q^{54} + 234462004 q^{55} - 937362336 q^{57} - 35348480 q^{58} + 336068664 q^{59} - 88408064 q^{60} + 54683228 q^{61} - 267288192 q^{62} - 1276041836 q^{63} - 6039797760 q^{64} - 57260282 q^{65} - 62464000 q^{66} - 175471280 q^{67} - 1386840064 q^{68} + 1121140464 q^{69} + 609992224 q^{70} + 2578447192 q^{71} - 70746112 q^{72} - 1392719328 q^{73} + 450601216 q^{74} + 4828166690 q^{75} + 1067589632 q^{76} + 1135132908 q^{77} - 260402944 q^{78} - 1003003648 q^{79} + 37224448 q^{80} + 8580074056 q^{81} - 1806990336 q^{82} + 1525742812 q^{83} - 494696448 q^{84} + 1142555716 q^{85} - 312537792 q^{86} - 3465043916 q^{87} - 844701696 q^{88} + 248892264 q^{89} + 1904412160 q^{90} + 2941626216 q^{91} + 1009893376 q^{92} + 3371917528 q^{93} + 1010944000 q^{94} + 2353679394 q^{95} + 339738624 q^{96} + 10847335596 q^{97} + 4189254656 q^{98} + 5152718576 q^{99} + O(q^{100}) \)

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

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