↑

Properties

Label 1848.2.cw
Level $1848$
Weight $2$
Character orbit 1848.cw
Rep. character $\chi_{1848}(377,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $384$
Sturm bound $768$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1848 = 2^{3} \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1848.cw (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1848, [\chi])\).

Total New Old
Modular forms 1600 384 1216
Cusp forms 1472 384 1088
Eisenstein series 128 0 128

Trace form

\( 384 q + 4 q^{7} + O(q^{10}) \) \( 384 q + 4 q^{7} + 8 q^{21} - 60 q^{25} + 16 q^{37} + 36 q^{39} - 8 q^{49} - 36 q^{51} - 48 q^{57} + 24 q^{63} + 64 q^{67} - 56 q^{79} + 32 q^{81} + 28 q^{85} + 40 q^{91} - 56 q^{93} - 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1848, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1848, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1848, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(924, [\chi])\)\(^{\oplus 2}\)