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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
552.2.q.a \(30\) \(4.408\) None \(0\) \(-3\) \(0\) \(-2\)
552.2.q.b \(30\) \(4.408\) None \(0\) \(-3\) \(0\) \(0\)
552.2.q.c \(30\) \(4.408\) None \(0\) \(3\) \(-2\) \(-2\)
552.2.q.d \(30\) \(4.408\) None \(0\) \(3\) \(2\) \(4\)

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

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