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Properties

Label 552.2.q
Level $552$
Weight $2$
Character orbit 552.q
Rep. character $\chi_{552}(25,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $120$
Newform subspaces $4$
Sturm bound $192$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 552.q (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 4 \)
Sturm bound: \(192\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(552, [\chi])\).

Total New Old
Modular forms 1040 120 920
Cusp forms 880 120 760
Eisenstein series 160 0 160

Trace form

\( 120 q - 12 q^{9} + O(q^{10}) \) \( 120 q - 12 q^{9} - 8 q^{11} + 4 q^{19} - 4 q^{21} + 8 q^{23} - 20 q^{25} - 16 q^{31} - 4 q^{33} + 44 q^{35} + 24 q^{37} + 36 q^{39} + 60 q^{41} + 32 q^{43} + 96 q^{47} + 4 q^{49} + 48 q^{51} + 36 q^{53} + 76 q^{55} + 32 q^{57} + 44 q^{59} - 20 q^{61} + 12 q^{67} - 4 q^{69} + 8 q^{71} - 24 q^{73} - 16 q^{75} - 116 q^{79} - 12 q^{81} - 100 q^{83} - 100 q^{85} + 24 q^{87} - 84 q^{89} - 280 q^{91} + 16 q^{93} - 224 q^{95} - 148 q^{97} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(552, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
552.2.q.a 552.q 23.c $30$ $4.408$ None \(0\) \(-3\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{11}]$
552.2.q.b 552.q 23.c $30$ $4.408$ None \(0\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{11}]$
552.2.q.c 552.q 23.c $30$ $4.408$ None \(0\) \(3\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{11}]$
552.2.q.d 552.q 23.c $30$ $4.408$ None \(0\) \(3\) \(2\) \(4\) $\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{2}^{\mathrm{old}}(552, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(552, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(276, [\chi])\)\(^{\oplus 2}\)