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Properties

Label 350.10.j
Level $350$
Weight $10$
Character orbit 350.j
Rep. character $\chi_{350}(149,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $216$
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.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(600\)

Dimensions

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

Total New Old
Modular forms 1104 216 888
Cusp forms 1056 216 840
Eisenstein series 48 0 48

Trace form

\( 216 q + 27648 q^{4} + 1280 q^{6} + 738992 q^{9} + O(q^{10}) \) \( 216 q + 27648 q^{4} + 1280 q^{6} + 738992 q^{9} + 10340 q^{11} - 319424 q^{14} - 7077888 q^{16} + 866384 q^{19} + 2373596 q^{21} + 163840 q^{24} - 4718848 q^{26} - 24766728 q^{29} - 10306940 q^{31} - 21381376 q^{34} + 378363904 q^{36} + 76884128 q^{39} + 104280304 q^{41} - 2647040 q^{44} + 2933888 q^{46} + 4609440 q^{49} + 77985412 q^{51} - 31901888 q^{54} - 65683456 q^{56} + 252190444 q^{59} - 413584472 q^{61} - 3623878656 q^{64} + 62464000 q^{66} - 3371415032 q^{69} - 198004016 q^{71} + 498060480 q^{74} + 443588608 q^{76} - 655496028 q^{79} - 6614319140 q^{81} + 1233307648 q^{84} - 737522432 q^{86} + 2736630292 q^{89} - 1364862088 q^{91} - 974805056 q^{94} - 41943040 q^{96} + 1699124760 q^{99} + O(q^{100}) \)

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

\( S_{10}^{\mathrm{old}}(350, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)