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Properties

Label 828.2.i
Level $828$
Weight $2$
Character orbit 828.i
Rep. character $\chi_{828}(277,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $44$
Newform subspaces $4$
Sturm bound $288$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 828.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(288\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(828, [\chi])\).

Total New Old
Modular forms 300 44 256
Cusp forms 276 44 232
Eisenstein series 24 0 24

Trace form

\( 44 q + 2 q^{3} - 2 q^{7} + 10 q^{9} + O(q^{10}) \) \( 44 q + 2 q^{3} - 2 q^{7} + 10 q^{9} + 2 q^{11} - 2 q^{13} - 10 q^{15} - 8 q^{17} + 16 q^{19} + 8 q^{21} - 22 q^{25} + 2 q^{27} + 4 q^{29} + 4 q^{31} + 12 q^{35} + 4 q^{37} + 14 q^{41} - 2 q^{43} - 4 q^{45} + 10 q^{47} - 24 q^{49} - 20 q^{51} + 40 q^{53} - 24 q^{55} + 16 q^{57} - 2 q^{59} - 14 q^{61} + 18 q^{63} - 28 q^{65} - 20 q^{67} + 36 q^{71} + 40 q^{73} + 4 q^{75} + 8 q^{77} + 22 q^{79} + 34 q^{81} + 12 q^{83} + 36 q^{85} - 2 q^{87} - 48 q^{89} - 4 q^{91} + 24 q^{93} - 12 q^{95} + 16 q^{97} + 54 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(828, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
828.2.i.a 828.i 9.c $6$ $6.612$ 6.0.309123.1 None \(0\) \(-2\) \(2\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{2}+\beta _{4})q^{3}+(-\beta _{1}-2\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
828.2.i.b 828.i 9.c $10$ $6.612$ 10.0.\(\cdots\).1 None \(0\) \(3\) \(6\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{3}+(-\beta _{2}+\beta _{3}-\beta _{7})q^{5}+(-1+\cdots)q^{7}+\cdots\)
828.2.i.c 828.i 9.c $12$ $6.612$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-2\) \(-6\) \(10\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{11})q^{3}+(1-\beta _{3}+\beta _{6}-\beta _{8}+\cdots)q^{5}+\cdots\)
828.2.i.d 828.i 9.c $16$ $6.612$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(3\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{7}q^{3}+(\beta _{4}-\beta _{6}-\beta _{9}+\beta _{12})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(828, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(828, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(414, [\chi])\)\(^{\oplus 2}\)