Properties

Label 770.2.bg
Level $770$
Weight $2$
Character orbit 770.bg
Rep. character $\chi_{770}(81,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $256$
Newform subspaces $6$
Sturm bound $288$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.bg (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{15})\)
Newform subspaces: \( 6 \)
Sturm bound: \(288\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(770, [\chi])\).

Total New Old
Modular forms 1216 256 960
Cusp forms 1088 256 832
Eisenstein series 128 0 128

Trace form

\( 256q + 32q^{4} + 44q^{9} + O(q^{10}) \) \( 256q + 32q^{4} + 44q^{9} + 16q^{10} - 2q^{11} + 16q^{13} - 2q^{14} - 24q^{15} + 32q^{16} - 28q^{17} + 16q^{18} + 4q^{19} + 32q^{21} - 8q^{22} + 24q^{23} + 32q^{25} - 20q^{26} + 72q^{27} + 40q^{29} - 16q^{33} + 64q^{34} - 4q^{35} - 48q^{36} + 8q^{37} + 8q^{38} + 4q^{39} - 4q^{40} + 84q^{41} + 40q^{42} - 2q^{44} + 4q^{46} + 8q^{47} + 20q^{49} + 4q^{51} - 8q^{52} - 8q^{53} - 16q^{55} - 80q^{57} + 8q^{58} + 16q^{59} - 8q^{60} + 56q^{61} + 16q^{62} - 64q^{63} - 64q^{64} - 4q^{65} - 32q^{67} - 28q^{68} - 320q^{69} + 64q^{71} - 24q^{72} - 52q^{73} - 20q^{74} - 8q^{76} - 84q^{77} - 192q^{78} - 44q^{79} - 20q^{81} - 40q^{82} - 144q^{83} - 72q^{84} + 48q^{85} - 16q^{86} - 104q^{87} - 16q^{88} - 72q^{89} + 40q^{90} + 58q^{91} + 72q^{92} - 4q^{93} - 42q^{94} - 128q^{97} - 64q^{98} + 148q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(770, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
770.2.bg.a \(8\) \(6.148\) \(\Q(\zeta_{15})\) None \(-1\) \(1\) \(-1\) \(-4\) \(q-\zeta_{15}q^{2}+(2-\zeta_{15}+2\zeta_{15}^{3}-2\zeta_{15}^{4}+\cdots)q^{3}+\cdots\)
770.2.bg.b \(8\) \(6.148\) \(\Q(\zeta_{15})\) None \(1\) \(-1\) \(1\) \(-4\) \(q+\zeta_{15}q^{2}+(-2+\zeta_{15}-2\zeta_{15}^{3}+2\zeta_{15}^{4}+\cdots)q^{3}+\cdots\)
770.2.bg.c \(48\) \(6.148\) None \(-6\) \(-4\) \(-6\) \(12\)
770.2.bg.d \(48\) \(6.148\) None \(6\) \(4\) \(6\) \(-4\)
770.2.bg.e \(72\) \(6.148\) None \(-9\) \(3\) \(9\) \(2\)
770.2.bg.f \(72\) \(6.148\) None \(9\) \(-3\) \(-9\) \(-2\)

Decomposition of \(S_{2}^{\mathrm{old}}(770, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(770, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)