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Properties

Label 944.2.m
Level $944$
Weight $2$
Character orbit 944.m
Rep. character $\chi_{944}(17,\cdot)$
Character field $\Q(\zeta_{29})$
Dimension $812$
Newform subspaces $6$
Sturm bound $240$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 944 = 2^{4} \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 944.m (of order \(29\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 59 \)
Character field: \(\Q(\zeta_{29})\)
Newform subspaces: \( 6 \)
Sturm bound: \(240\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(944, [\chi])\).

Total New Old
Modular forms 3528 868 2660
Cusp forms 3192 812 2380
Eisenstein series 336 56 280

Trace form

\( 812 q + 27 q^{3} - 27 q^{5} + 27 q^{7} - 58 q^{9} + O(q^{10}) \) \( 812 q + 27 q^{3} - 27 q^{5} + 27 q^{7} - 58 q^{9} + 33 q^{11} - 27 q^{13} + 33 q^{15} - 31 q^{17} + 27 q^{19} - 21 q^{21} + 21 q^{23} - 60 q^{25} + 21 q^{27} - 27 q^{29} + 21 q^{31} - 29 q^{33} + 5 q^{35} - 27 q^{37} + q^{39} - 31 q^{41} + 17 q^{43} - 11 q^{45} + 29 q^{47} - 66 q^{49} + q^{51} - 35 q^{53} - 7 q^{55} - 37 q^{57} + 20 q^{59} - 35 q^{61} + 5 q^{63} - 41 q^{65} + 21 q^{67} - 21 q^{69} + 23 q^{71} - 47 q^{73} + 25 q^{75} - 21 q^{77} + 39 q^{79} - 66 q^{81} + 37 q^{83} - 17 q^{85} + 45 q^{87} - 39 q^{89} + 9 q^{91} + 3 q^{93} + 47 q^{95} - 31 q^{97} + 57 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(944, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
944.2.m.a 944.m 59.c $56$ $7.538$ None 118.2.c.a \(0\) \(1\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{29}]$
944.2.m.b 944.m 59.c $84$ $7.538$ None 118.2.c.b \(0\) \(5\) \(-5\) \(8\) $\mathrm{SU}(2)[C_{29}]$
944.2.m.c 944.m 59.c $112$ $7.538$ None 59.2.c.a \(0\) \(23\) \(-25\) \(23\) $\mathrm{SU}(2)[C_{29}]$
944.2.m.d 944.m 59.c $140$ $7.538$ None 236.2.e.a \(0\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{29}]$
944.2.m.e 944.m 59.c $196$ $7.538$ None 472.2.i.a \(0\) \(-3\) \(3\) \(-4\) $\mathrm{SU}(2)[C_{29}]$
944.2.m.f 944.m 59.c $224$ $7.538$ None 472.2.i.b \(0\) \(1\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{29}]$

Decomposition of \(S_{2}^{\mathrm{old}}(944, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(944, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(118, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(236, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(472, [\chi])\)\(^{\oplus 2}\)