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Properties

Label 350.10.o
Level $350$
Weight $10$
Character orbit 350.o
Rep. character $\chi_{350}(143,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $432$
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.o (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(600\)

Dimensions

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

Total New Old
Modular forms 2208 432 1776
Cusp forms 2112 432 1680
Eisenstein series 96 0 96

Trace form

\( 432 q + 2132 q^{7} + O(q^{10}) \) \( 432 q + 2132 q^{7} - 237144 q^{11} + 14155776 q^{16} - 3157344 q^{17} - 276352 q^{18} - 5331336 q^{21} + 2130048 q^{22} + 566524 q^{23} + 4589184 q^{26} - 6401024 q^{28} + 35600928 q^{31} - 46709268 q^{33} - 694460416 q^{36} + 34038456 q^{37} + 52162176 q^{38} - 110817856 q^{42} + 66887488 q^{43} + 97963264 q^{46} - 41977272 q^{47} - 319155312 q^{51} + 72980608 q^{53} + 131366912 q^{56} - 444525088 q^{57} - 309943808 q^{58} + 355743576 q^{61} + 1019604156 q^{63} - 117911152 q^{67} - 808280064 q^{68} + 469051072 q^{71} - 70746112 q^{72} + 2966047632 q^{73} + 1855751204 q^{77} + 260402944 q^{78} + 8021313160 q^{81} - 1355242752 q^{82} - 852176256 q^{86} + 1844903484 q^{87} + 272646144 q^{88} - 3776976192 q^{91} - 290060288 q^{92} - 5039370768 q^{93} + 1786773504 q^{96} + 4665322880 q^{98} + O(q^{100}) \)

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

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