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Properties

Label 350.4.r
Level $350$
Weight $4$
Character orbit 350.r
Rep. character $\chi_{350}(13,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $480$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 350.r (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(350, [\chi])\).

Total New Old
Modular forms 1472 480 992
Cusp forms 1408 480 928
Eisenstein series 64 0 64

Trace form

\( 480 q - 4 q^{7} + O(q^{10}) \) \( 480 q - 4 q^{7} - 504 q^{15} + 1920 q^{16} + 16 q^{18} + 912 q^{22} + 544 q^{23} - 520 q^{25} - 224 q^{28} + 160 q^{29} + 144 q^{30} + 2348 q^{35} + 4320 q^{36} + 456 q^{37} + 2440 q^{39} - 1280 q^{42} + 1824 q^{43} + 448 q^{50} - 704 q^{53} - 4704 q^{57} - 992 q^{58} - 352 q^{60} - 5740 q^{63} + 3312 q^{65} + 1088 q^{67} + 2304 q^{70} + 64 q^{72} + 7752 q^{77} + 80 q^{78} + 9720 q^{81} - 960 q^{84} - 5072 q^{85} - 768 q^{88} - 1344 q^{92} - 10032 q^{93} + 5136 q^{95} + 4064 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(350, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(350, [\chi])\) into lower level spaces

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