Properties

Label 690.2.m
Level $690$
Weight $2$
Character orbit 690.m
Rep. character $\chi_{690}(31,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $160$
Newform subspaces $8$
Sturm bound $288$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.m (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 8 \)
Sturm bound: \(288\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(690, [\chi])\).

Total New Old
Modular forms 1520 160 1360
Cusp forms 1360 160 1200
Eisenstein series 160 0 160

Trace form

\( 160q - 16q^{4} - 16q^{9} + O(q^{10}) \) \( 160q - 16q^{4} - 16q^{9} - 4q^{10} - 24q^{11} - 16q^{13} - 8q^{14} - 16q^{16} + 56q^{17} + 64q^{19} + 80q^{22} - 24q^{23} - 16q^{25} + 64q^{26} + 64q^{29} - 4q^{30} + 40q^{31} - 8q^{33} - 24q^{34} + 28q^{35} - 16q^{36} - 40q^{37} - 32q^{38} + 36q^{39} - 4q^{40} + 40q^{41} - 24q^{42} + 64q^{43} - 24q^{44} - 24q^{46} - 48q^{47} - 64q^{49} + 56q^{51} - 16q^{52} + 56q^{53} + 20q^{55} - 8q^{56} - 8q^{57} + 24q^{58} - 20q^{59} + 40q^{61} - 16q^{62} - 16q^{64} - 24q^{65} - 24q^{66} + 32q^{67} - 32q^{68} - 24q^{69} - 104q^{71} - 24q^{73} - 8q^{74} - 24q^{76} - 48q^{77} - 16q^{78} + 104q^{79} - 16q^{81} + 56q^{82} + 8q^{83} - 8q^{85} - 32q^{86} - 16q^{87} - 8q^{88} - 4q^{90} - 128q^{91} - 24q^{92} - 16q^{93} - 16q^{94} - 32q^{95} + 8q^{97} - 32q^{98} - 24q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(690, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
690.2.m.a \(10\) \(5.510\) \(\Q(\zeta_{22})\) None \(-1\) \(-1\) \(1\) \(0\) \(q+\zeta_{22}^{4}q^{2}+(-1+\zeta_{22}-\zeta_{22}^{2}+\zeta_{22}^{3}+\cdots)q^{3}+\cdots\)
690.2.m.b \(10\) \(5.510\) \(\Q(\zeta_{22})\) None \(1\) \(-1\) \(-1\) \(0\) \(q-\zeta_{22}^{4}q^{2}+(-1+\zeta_{22}-\zeta_{22}^{2}+\zeta_{22}^{3}+\cdots)q^{3}+\cdots\)
690.2.m.c \(20\) \(5.510\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-2\) \(2\) \(-2\) \(2\) \(q+\beta _{16}q^{2}-\beta _{14}q^{3}-\beta _{12}q^{4}+\beta _{11}q^{5}+\cdots\)
690.2.m.d \(20\) \(5.510\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-2\) \(2\) \(2\) \(2\) \(q+\beta _{7}q^{2}-\beta _{12}q^{3}+\beta _{10}q^{4}-\beta _{6}q^{5}+\cdots\)
690.2.m.e \(20\) \(5.510\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(2\) \(2\) \(-2\) \(-2\) \(q-\beta _{13}q^{2}-\beta _{16}q^{3}-\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
690.2.m.f \(20\) \(5.510\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(2\) \(2\) \(2\) \(-2\) \(q+\beta _{8}q^{2}+(1+\beta _{5}+\beta _{6}-\beta _{7}-\beta _{8}+\cdots)q^{3}+\cdots\)
690.2.m.g \(30\) \(5.510\) None \(-3\) \(-3\) \(-3\) \(-8\)
690.2.m.h \(30\) \(5.510\) None \(3\) \(-3\) \(3\) \(8\)

Decomposition of \(S_{2}^{\mathrm{old}}(690, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(690, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 2}\)