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Properties

Label 952.2.q
Level $952$
Weight $2$
Character orbit 952.q
Rep. character $\chi_{952}(137,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $64$
Newform subspaces $6$
Sturm bound $288$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 952 = 2^{3} \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 952.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 6 \)
Sturm bound: \(288\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(952, [\chi])\).

Total New Old
Modular forms 304 64 240
Cusp forms 272 64 208
Eisenstein series 32 0 32

Trace form

\( 64 q + 4 q^{3} - 4 q^{5} - 28 q^{9} + O(q^{10}) \) \( 64 q + 4 q^{3} - 4 q^{5} - 28 q^{9} + 4 q^{11} + 8 q^{13} + 8 q^{15} - 4 q^{17} + 8 q^{21} - 8 q^{23} - 44 q^{25} - 32 q^{27} + 24 q^{29} - 12 q^{31} - 8 q^{33} - 8 q^{35} - 4 q^{37} - 12 q^{39} + 48 q^{41} + 24 q^{43} - 8 q^{45} - 20 q^{49} + 4 q^{53} - 16 q^{55} - 72 q^{57} - 4 q^{59} + 8 q^{61} + 32 q^{63} + 24 q^{65} - 4 q^{67} - 32 q^{69} - 32 q^{71} + 12 q^{73} + 28 q^{75} - 24 q^{77} - 12 q^{79} - 4 q^{81} + 20 q^{87} + 20 q^{89} - 48 q^{91} - 16 q^{93} + 16 q^{95} - 40 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(952, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
952.2.q.a 952.q 7.c $2$ $7.602$ \(\Q(\sqrt{-3}) \) None 952.2.q.a \(0\) \(0\) \(1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
952.2.q.b 952.q 7.c $2$ $7.602$ \(\Q(\sqrt{-3}) \) None 952.2.q.b \(0\) \(3\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-3\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
952.2.q.c 952.q 7.c $12$ $7.602$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 952.2.q.c \(0\) \(-1\) \(-1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{3}-\beta _{11}q^{5}+(\beta _{2}-\beta _{6}-\beta _{9}+\cdots)q^{7}+\cdots\)
952.2.q.d 952.q 7.c $14$ $7.602$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None 952.2.q.d \(0\) \(0\) \(1\) \(-7\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}+(\beta _{3}-\beta _{10})q^{5}+(-\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots\)
952.2.q.e 952.q 7.c $14$ $7.602$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 952.2.q.e \(0\) \(3\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}-\beta _{13}q^{5}+(\beta _{4}-\beta _{7}+\beta _{10}+\cdots)q^{7}+\cdots\)
952.2.q.f 952.q 7.c $20$ $7.602$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 952.2.q.f \(0\) \(-1\) \(-1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{2})q^{3}+\beta _{12}q^{5}+\beta _{18}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(952, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(952, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(476, [\chi])\)\(^{\oplus 2}\)