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Properties

Label 828.2.q
Level $828$
Weight $2$
Character orbit 828.q
Rep. character $\chi_{828}(73,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $100$
Newform subspaces $4$
Sturm bound $288$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 828.q (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 4 \)
Sturm bound: \(288\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 1560 100 1460
Cusp forms 1320 100 1220
Eisenstein series 240 0 240

Trace form

\( 100 q + 2 q^{5} + 2 q^{7} + O(q^{10}) \) \( 100 q + 2 q^{5} + 2 q^{7} + 2 q^{11} - 2 q^{13} - q^{17} - 19 q^{19} - 22 q^{23} - 16 q^{25} - 5 q^{29} + 3 q^{31} + 14 q^{35} - 22 q^{37} + 8 q^{41} - 44 q^{43} + 46 q^{47} + 44 q^{49} + 34 q^{53} - 18 q^{55} + 38 q^{59} + 32 q^{61} + 71 q^{65} + 56 q^{67} + 37 q^{71} + 32 q^{73} + 31 q^{77} + 58 q^{79} + 53 q^{83} + 44 q^{85} + 46 q^{89} + 50 q^{91} + 53 q^{95} - 25 q^{97} + O(q^{100}) \)

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.q.a 828.q 23.c $20$ $6.612$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{11}]$ \(q+(-\beta _{2}+\beta _{10}+\beta _{11}+\beta _{13}-\beta _{15}+\cdots)q^{5}+\cdots\)
828.2.q.b 828.q 23.c $20$ $6.612$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{11}]$ \(q+(-\beta _{6}+\beta _{7}+\beta _{8}-\beta _{14}-\beta _{17})q^{5}+\cdots\)
828.2.q.c 828.q 23.c $20$ $6.612$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{11}]$ \(q+(1-\beta _{8}-\beta _{9}-\beta _{10}+\beta _{11}+\beta _{12}+\cdots)q^{5}+\cdots\)
828.2.q.d 828.q 23.c $40$ $6.612$ None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{11}]$

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

\( S_{2}^{\mathrm{old}}(828, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(276, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(414, [\chi])\)\(^{\oplus 2}\)