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Properties

Label 152.2.i
Level $152$
Weight $2$
Character orbit 152.i
Rep. character $\chi_{152}(49,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $10$
Newform subspaces $3$
Sturm bound $40$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 152.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
Sturm bound: \(40\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(152, [\chi])\).

Total New Old
Modular forms 48 10 38
Cusp forms 32 10 22
Eisenstein series 16 0 16

Trace form

\( 10 q - 3 q^{3} - 4 q^{7} - 2 q^{9} + O(q^{10}) \) \( 10 q - 3 q^{3} - 4 q^{7} - 2 q^{9} + 6 q^{11} + 4 q^{13} - 4 q^{15} - 8 q^{17} + 9 q^{19} + 6 q^{21} - 6 q^{23} - 9 q^{25} + 18 q^{27} + 4 q^{29} - 24 q^{31} - 5 q^{33} - 12 q^{35} - 16 q^{37} - 8 q^{39} + 15 q^{41} + 10 q^{43} - 8 q^{45} - 6 q^{49} - 20 q^{51} + 16 q^{53} + 14 q^{55} - 38 q^{57} - 25 q^{59} + 12 q^{61} + 40 q^{63} - 4 q^{65} + 5 q^{67} + 20 q^{69} + 8 q^{71} + 29 q^{73} + 6 q^{75} + 20 q^{77} + 6 q^{79} - 25 q^{81} + 46 q^{83} + 6 q^{85} + 64 q^{87} + 12 q^{89} - 44 q^{91} - 36 q^{93} + 42 q^{95} + 11 q^{97} - 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(152, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
152.2.i.a 152.i 19.c $2$ $1.214$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
152.2.i.b 152.i 19.c $2$ $1.214$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(4-4\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
152.2.i.c 152.i 19.c $6$ $1.214$ 6.0.2696112.1 None \(0\) \(-1\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{5})q^{3}-\beta _{1}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(152, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(152, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)