Properties

Label 819.2.fm
Level $819$
Weight $2$
Character orbit 819.fm
Rep. character $\chi_{819}(370,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $176$
Newform subspaces $8$
Sturm bound $224$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.fm (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 8 \)
Sturm bound: \(224\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(5\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(819, [\chi])\).

Total New Old
Modular forms 480 192 288
Cusp forms 416 176 240
Eisenstein series 64 16 48

Trace form

\( 176q + 8q^{2} - 12q^{4} - 4q^{7} + 16q^{8} + O(q^{10}) \) \( 176q + 8q^{2} - 12q^{4} - 4q^{7} + 16q^{8} + 20q^{11} - 16q^{14} + 60q^{16} + 4q^{22} + 12q^{23} - 8q^{28} + 4q^{29} + 36q^{32} + 28q^{35} - 4q^{37} - 72q^{43} - 8q^{44} - 92q^{46} - 36q^{49} - 132q^{50} + 40q^{53} + 120q^{56} - 48q^{58} - 36q^{65} + 40q^{67} + 80q^{70} - 60q^{71} + 40q^{74} - 16q^{79} - 44q^{85} + 96q^{86} + 204q^{88} - 12q^{91} + 56q^{92} - 12q^{95} - 4q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(819, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
819.2.fm.a \(4\) \(6.540\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(-2\) \(0\) \(q+(-1+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
819.2.fm.b \(4\) \(6.540\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(2\) \(-2\) \(q+(-1+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
819.2.fm.c \(4\) \(6.540\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q-2\zeta_{12}q^{4}+(2\zeta_{12}-3\zeta_{12}^{3})q^{7}+(3\zeta_{12}+\cdots)q^{13}+\cdots\)
819.2.fm.d \(4\) \(6.540\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(10\) \(q-2\zeta_{12}q^{4}+(2+\zeta_{12}^{2})q^{7}+(-3\zeta_{12}+\cdots)q^{13}+\cdots\)
819.2.fm.e \(32\) \(6.540\) None \(2\) \(0\) \(-2\) \(2\)
819.2.fm.f \(32\) \(6.540\) None \(2\) \(0\) \(2\) \(-2\)
819.2.fm.g \(32\) \(6.540\) None \(8\) \(0\) \(0\) \(0\)
819.2.fm.h \(64\) \(6.540\) None \(0\) \(0\) \(0\) \(-12\)

Decomposition of \(S_{2}^{\mathrm{old}}(819, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(819, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)