Properties

Label 882.2.z
Level $882$
Weight $2$
Character orbit 882.z
Rep. character $\chi_{882}(37,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $288$
Newform subspaces $8$
Sturm bound $336$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.z (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Newform subspaces: \( 8 \)
Sturm bound: \(336\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(882, [\chi])\).

Total New Old
Modular forms 2112 288 1824
Cusp forms 1920 288 1632
Eisenstein series 192 0 192

Trace form

\( 288q + 24q^{4} - 4q^{5} - 4q^{7} + O(q^{10}) \) \( 288q + 24q^{4} - 4q^{5} - 4q^{7} + 4q^{10} - 18q^{11} + 8q^{14} + 24q^{16} - 10q^{17} - 6q^{19} - 6q^{20} + 14q^{22} + 46q^{23} + 28q^{25} - 18q^{26} - 4q^{28} + 22q^{29} - 12q^{31} - 16q^{34} - 22q^{35} + 44q^{37} + 16q^{38} - 24q^{40} + 56q^{41} + 32q^{43} + 24q^{44} + 76q^{46} + 68q^{47} - 84q^{49} - 8q^{50} - 14q^{52} + 134q^{53} - 34q^{55} + 24q^{56} - 84q^{58} + 50q^{59} - 136q^{61} + 36q^{62} - 48q^{64} - 12q^{67} + 32q^{68} - 14q^{70} + 34q^{71} - 26q^{73} - 14q^{74} - 16q^{76} - 70q^{77} - 8q^{79} + 10q^{80} + 80q^{83} + 32q^{85} - 50q^{86} - 14q^{88} + 84q^{89} + 66q^{91} - 8q^{92} + 10q^{94} + 116q^{95} + 12q^{97} + 52q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(882, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
882.2.z.a \(24\) \(7.043\) None \(-2\) \(0\) \(-1\) \(0\)
882.2.z.b \(24\) \(7.043\) None \(-2\) \(0\) \(0\) \(0\)
882.2.z.c \(24\) \(7.043\) None \(2\) \(0\) \(-1\) \(0\)
882.2.z.d \(24\) \(7.043\) None \(2\) \(0\) \(0\) \(0\)
882.2.z.e \(36\) \(7.043\) None \(-3\) \(0\) \(0\) \(-1\)
882.2.z.f \(36\) \(7.043\) None \(3\) \(0\) \(-2\) \(-5\)
882.2.z.g \(60\) \(7.043\) None \(-5\) \(0\) \(-3\) \(1\)
882.2.z.h \(60\) \(7.043\) None \(5\) \(0\) \(3\) \(1\)

Decomposition of \(S_{2}^{\mathrm{old}}(882, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(882, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)