↑

Properties

Label 1900.3.cg
Level $1900$
Weight $3$
Character orbit 1900.cg
Rep. character $\chi_{1900}(197,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1600$
Sturm bound $900$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1900.cg (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(900\)

Dimensions

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

Total New Old
Modular forms 9696 1600 8096
Cusp forms 9504 1600 7904
Eisenstein series 192 0 192

Trace form

\( 1600 q - 2 q^{5} + 12 q^{7} + O(q^{10}) \) \( 1600 q - 2 q^{5} + 12 q^{7} + 8 q^{13} + 6 q^{15} - 38 q^{17} - 100 q^{19} + 80 q^{23} + 50 q^{25} + 84 q^{27} - 100 q^{29} - 192 q^{33} + 34 q^{35} + 128 q^{37} + 800 q^{39} - 298 q^{43} + 756 q^{45} - 150 q^{47} + 82 q^{53} - 344 q^{55} + 958 q^{57} + 400 q^{59} - 1034 q^{63} + 1520 q^{65} - 488 q^{67} + 292 q^{73} + 52 q^{75} + 60 q^{77} - 1800 q^{81} - 540 q^{83} - 144 q^{85} - 820 q^{87} + 464 q^{93} + 468 q^{95} + 122 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{3}^{\mathrm{old}}(1900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 2}\)