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Properties

Label 912.3.by
Level $912$
Weight $3$
Character orbit 912.by
Rep. character $\chi_{912}(97,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $240$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 912.by (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(912, [\chi])\).

Total New Old
Modular forms 1992 240 1752
Cusp forms 1848 240 1608
Eisenstein series 144 0 144

Trace form

\( 240 q + O(q^{10}) \) \( 240 q + 48 q^{19} + 48 q^{41} - 48 q^{43} - 288 q^{47} - 840 q^{49} - 144 q^{51} + 48 q^{53} - 144 q^{55} - 144 q^{61} - 144 q^{63} + 720 q^{65} - 480 q^{67} - 432 q^{69} - 288 q^{71} + 120 q^{73} + 336 q^{79} + 864 q^{83} + 432 q^{85} + 432 q^{87} - 720 q^{89} + 192 q^{91} - 480 q^{95} + 144 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(912, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(912, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)