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Properties

Label 350.7.w
Level $350$
Weight $7$
Character orbit 350.w
Rep. character $\chi_{350}(23,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1920$
Sturm bound $420$

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Defining parameters

Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 350.w (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(420\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(350, [\chi])\).

Total New Old
Modular forms 5824 1920 3904
Cusp forms 5696 1920 3776
Eisenstein series 128 0 128

Trace form

\( 1920 q - 224 q^{5} - 696 q^{7} + O(q^{10}) \) \( 1920 q - 224 q^{5} - 696 q^{7} - 1344 q^{10} + 5712 q^{15} - 245760 q^{16} - 26432 q^{17} + 2432 q^{18} - 148224 q^{22} + 62528 q^{23} - 4896 q^{25} - 321552 q^{27} - 70656 q^{28} + 99200 q^{29} + 111936 q^{30} + 58184 q^{33} - 197872 q^{35} - 3732480 q^{36} - 184032 q^{37} - 68992 q^{38} - 414800 q^{39} + 25408 q^{42} + 297600 q^{43} - 743008 q^{45} - 146720 q^{47} + 306432 q^{50} - 733984 q^{53} + 1450848 q^{55} + 529312 q^{57} - 716160 q^{58} - 1262800 q^{59} - 230912 q^{60} - 4474176 q^{62} - 1984464 q^{63} + 1388000 q^{65} + 931680 q^{67} - 1662976 q^{68} + 11211200 q^{69} + 2377536 q^{70} + 77824 q^{72} - 2092272 q^{73} + 2593136 q^{75} - 4283576 q^{77} - 594176 q^{78} + 229376 q^{80} - 14171760 q^{81} + 1677312 q^{82} + 2625728 q^{83} + 1459200 q^{84} + 1695888 q^{85} - 4945528 q^{87} + 485376 q^{88} - 8568000 q^{89} - 3458560 q^{90} - 172032 q^{92} - 1465728 q^{93} + 4328608 q^{95} + 11503968 q^{97} + 6834304 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(350, [\chi])\) into newform subspaces

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

Decomposition of \(S_{7}^{\mathrm{old}}(350, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(350, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)