Properties

Label 735.2.bg
Level $735$
Weight $2$
Character orbit 735.bg
Rep. character $\chi_{735}(16,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $456$
Newform subspaces $4$
Sturm bound $224$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.bg (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Newform subspaces: \( 4 \)
Sturm bound: \(224\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(735, [\chi])\).

Total New Old
Modular forms 1392 456 936
Cusp forms 1296 456 840
Eisenstein series 96 0 96

Trace form

\( 456q - 2q^{3} + 40q^{4} - 2q^{7} + 38q^{9} + O(q^{10}) \) \( 456q - 2q^{3} + 40q^{4} - 2q^{7} + 38q^{9} - 4q^{10} + 4q^{11} - 4q^{12} + 4q^{13} + 4q^{14} + 52q^{16} + 8q^{17} + 6q^{19} - 16q^{20} + 12q^{21} - 40q^{22} + 96q^{24} + 38q^{25} + 36q^{26} + 4q^{27} + 60q^{28} - 24q^{29} + 6q^{31} + 20q^{32} - 8q^{33} + 72q^{34} + 20q^{35} - 80q^{36} + 76q^{37} - 144q^{38} + 36q^{39} - 12q^{40} - 64q^{41} - 108q^{42} + 12q^{43} - 92q^{44} + 24q^{46} - 104q^{47} - 96q^{48} - 42q^{49} - 52q^{51} - 168q^{52} - 80q^{53} + 24q^{55} - 132q^{56} - 12q^{57} - 76q^{58} - 32q^{59} + 46q^{61} - 136q^{62} + 12q^{63} - 72q^{64} + 12q^{65} + 12q^{66} + 2q^{67} - 12q^{68} - 24q^{69} + 4q^{70} + 48q^{71} + 94q^{73} + 48q^{74} - 2q^{75} - 40q^{76} + 40q^{77} - 24q^{78} + 10q^{79} + 16q^{80} + 38q^{81} - 252q^{82} + 76q^{83} - 48q^{84} - 8q^{85} - 368q^{86} - 24q^{87} + 212q^{88} - 156q^{89} + 8q^{90} - 38q^{91} - 16q^{92} + 6q^{93} - 284q^{94} + 8q^{95} + 192q^{96} - 192q^{97} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(735, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
735.2.bg.a \(108\) \(5.869\) None \(-1\) \(9\) \(9\) \(-13\)
735.2.bg.b \(108\) \(5.869\) None \(1\) \(9\) \(-9\) \(9\)
735.2.bg.c \(120\) \(5.869\) None \(-1\) \(-10\) \(10\) \(14\)
735.2.bg.d \(120\) \(5.869\) None \(1\) \(-10\) \(-10\) \(-12\)

Decomposition of \(S_{2}^{\mathrm{old}}(735, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(735, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)