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Properties

Label 350.10.g
Level $350$
Weight $10$
Character orbit 350.g
Rep. character $\chi_{350}(293,\cdot)$
Character field $\Q(\zeta_{4})$
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.g (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
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

\( 216 q - 2132 q^{7} + O(q^{10}) \) \( 216 q - 2132 q^{7} - 104400 q^{11} - 14155776 q^{16} + 276352 q^{18} - 4159968 q^{21} - 4172544 q^{22} - 3319792 q^{23} + 545792 q^{28} - 399140864 q^{36} + 9288408 q^{37} - 25349120 q^{42} - 164578192 q^{43} + 195926528 q^{46} + 101536176 q^{51} + 504816752 q^{53} - 32178176 q^{56} + 705684448 q^{57} - 101949184 q^{58} + 866678460 q^{63} - 322162496 q^{67} + 89985728 q^{71} + 70746112 q^{72} - 594520184 q^{77} - 1758371200 q^{78} - 11452688632 q^{81} - 3576268800 q^{86} + 1068171264 q^{88} - 2944404888 q^{91} - 849866752 q^{92} - 1849548024 q^{93} + 1830297088 q^{98} + O(q^{100}) \)

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

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