Properties

Label 3192.2.gu
Level $3192$
Weight $2$
Character orbit 3192.gu
Rep. character $\chi_{3192}(401,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $960$
Sturm bound $1280$

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Defining parameters

Level: \( N \) \(=\) \( 3192 = 2^{3} \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3192.gu (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 399 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(1280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3192, [\chi])\).

Total New Old
Modular forms 3936 960 2976
Cusp forms 3744 960 2784
Eisenstein series 192 0 192

Trace form

\( 960 q + O(q^{10}) \) \( 960 q - 6 q^{13} - 12 q^{15} + 12 q^{19} + 12 q^{25} - 36 q^{37} + 18 q^{39} + 42 q^{43} - 24 q^{57} + 12 q^{61} - 108 q^{63} - 12 q^{67} + 6 q^{73} - 42 q^{79} + 60 q^{85} + 72 q^{87} + 90 q^{91} - 36 q^{93} + 24 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3192, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3192, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3192, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(798, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1596, [\chi])\)\(^{\oplus 2}\)