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Properties

Label 3800.2.bp
Level $3800$
Weight $2$
Character orbit 3800.bp
Rep. character $\chi_{3800}(1201,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $570$
Sturm bound $1200$

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Defining parameters

Level: \( N \) \(=\) \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3800.bp (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 \(M_{2}(3800, [\chi])\).

Total New Old
Modular forms 3744 570 3174
Cusp forms 3456 570 2886
Eisenstein series 288 0 288

Trace form

\( 570 q + 3 q^{3} - 9 q^{9} + O(q^{10}) \) \( 570 q + 3 q^{3} - 9 q^{9} - 6 q^{13} + 6 q^{17} - 6 q^{19} - 6 q^{21} - 12 q^{23} - 27 q^{27} - 12 q^{29} - 6 q^{31} + 27 q^{33} + 12 q^{37} - 36 q^{39} - 3 q^{41} - 24 q^{47} - 291 q^{49} + 33 q^{51} - 18 q^{53} - 36 q^{57} + 27 q^{59} - 6 q^{61} + 102 q^{63} - 69 q^{67} - 24 q^{69} + 30 q^{71} + 54 q^{73} - 36 q^{77} + 156 q^{79} + 21 q^{81} + 36 q^{83} - 18 q^{87} - 36 q^{89} + 12 q^{91} - 42 q^{93} - 69 q^{97} - 99 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3800, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(760, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1900, [\chi])\)\(^{\oplus 2}\)