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Properties

Label 2850.2.v
Level $2850$
Weight $2$
Character orbit 2850.v
Rep. character $\chi_{2850}(301,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $384$
Sturm bound $1200$

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Defining parameters

Level: \( N \) \(=\) \( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2850.v (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(1200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2850, [\chi])\).

Total New Old
Modular forms 3744 384 3360
Cusp forms 3456 384 3072
Eisenstein series 288 0 288

Trace form

\( 384 q - 12 q^{7} + O(q^{10}) \) \( 384 q - 12 q^{7} - 12 q^{11} + 24 q^{14} - 12 q^{17} - 48 q^{19} - 48 q^{21} - 48 q^{23} + 12 q^{26} - 48 q^{29} - 12 q^{31} - 12 q^{33} + 12 q^{34} + 12 q^{38} - 36 q^{41} + 12 q^{42} + 48 q^{43} - 12 q^{44} - 12 q^{46} - 36 q^{47} - 228 q^{49} - 24 q^{53} + 24 q^{56} - 12 q^{57} - 24 q^{58} - 12 q^{59} + 84 q^{61} - 12 q^{62} - 192 q^{64} - 48 q^{67} - 12 q^{68} - 24 q^{69} - 84 q^{71} - 24 q^{73} - 36 q^{74} - 12 q^{76} + 120 q^{77} - 24 q^{78} + 60 q^{82} + 12 q^{83} - 12 q^{84} + 72 q^{86} + 12 q^{87} + 12 q^{88} + 156 q^{89} + 120 q^{91} + 60 q^{92} + 36 q^{93} + 72 q^{94} + 72 q^{97} + 120 q^{98} - 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2850, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1425, [\chi])\)\(^{\oplus 2}\)