Properties

Label 1900.3.u
Level $1900$
Weight $3$
Character orbit 1900.u
Rep. character $\chi_{1900}(601,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $128$
Sturm bound $900$

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Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1900.u (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(900\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1900, [\chi])\).

Total New Old
Modular forms 1236 128 1108
Cusp forms 1164 128 1036
Eisenstein series 72 0 72

Trace form

\( 128 q + 6 q^{3} + 196 q^{9} + O(q^{10}) \) \( 128 q + 6 q^{3} + 196 q^{9} - 14 q^{11} + 9 q^{13} + 19 q^{17} - 33 q^{19} - 18 q^{21} + 5 q^{23} - 45 q^{29} + 141 q^{33} + 78 q^{39} - 6 q^{41} - 51 q^{43} + 37 q^{47} + 1144 q^{49} - 27 q^{51} + 57 q^{53} + 293 q^{57} - 61 q^{61} + 4 q^{63} - 168 q^{67} + 147 q^{71} + 52 q^{73} - 132 q^{77} + 87 q^{79} - 600 q^{81} - 6 q^{83} + 126 q^{87} - 471 q^{89} + 348 q^{91} - 112 q^{93} - 114 q^{97} - 406 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1900, [\chi])\) into lower level spaces

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