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Properties

Label 3850.2.cz
Level $3850$
Weight $2$
Character orbit 3850.cz
Rep. character $\chi_{3850}(221,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $1600$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3850.cz (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3850, [\chi])\).

Total New Old
Modular forms 5824 1600 4224
Cusp forms 5696 1600 4096
Eisenstein series 128 0 128

Trace form

\( 1600 q + 200 q^{4} + 200 q^{9} + O(q^{10}) \) \( 1600 q + 200 q^{4} + 200 q^{9} - 88 q^{15} + 200 q^{16} + 24 q^{17} - 16 q^{18} - 24 q^{21} + 8 q^{23} - 8 q^{25} + 96 q^{26} - 192 q^{27} - 48 q^{29} + 4 q^{30} + 32 q^{34} + 4 q^{35} - 400 q^{36} + 16 q^{38} + 24 q^{39} + 48 q^{42} + 160 q^{43} + 12 q^{45} + 32 q^{50} + 24 q^{51} + 72 q^{53} - 16 q^{57} - 32 q^{58} - 48 q^{59} + 4 q^{60} + 72 q^{62} + 88 q^{63} - 400 q^{64} - 4 q^{65} - 16 q^{66} + 16 q^{67} - 96 q^{68} + 232 q^{69} + 8 q^{70} + 72 q^{71} - 16 q^{72} - 48 q^{73} - 32 q^{74} + 220 q^{75} - 32 q^{78} - 16 q^{79} + 224 q^{81} - 64 q^{82} + 232 q^{83} + 36 q^{84} - 208 q^{85} + 72 q^{87} - 48 q^{89} + 288 q^{90} + 56 q^{91} - 16 q^{92} + 104 q^{93} + 32 q^{94} + 68 q^{95} + 192 q^{97} + 80 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3850, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1925, [\chi])\)\(^{\oplus 2}\)