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Properties

Label 595.2.cm
Level $595$
Weight $2$
Character orbit 595.cm
Rep. character $\chi_{595}(88,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $1088$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 595 = 5 \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 595.cm (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 595 \)
Character field: \(\Q(\zeta_{48})\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(595, [\chi])\).

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

Trace form

\( 1088 q - 8 q^{2} - 8 q^{3} - 8 q^{5} - 64 q^{6} - 16 q^{7} - 64 q^{8} + O(q^{10}) \) \( 1088 q - 8 q^{2} - 8 q^{3} - 8 q^{5} - 64 q^{6} - 16 q^{7} - 64 q^{8} - 8 q^{10} - 16 q^{11} + 40 q^{12} + 64 q^{14} - 80 q^{15} - 8 q^{17} - 16 q^{18} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 8 q^{23} - 80 q^{26} - 128 q^{27} - 112 q^{28} - 72 q^{30} - 16 q^{31} - 72 q^{32} - 32 q^{35} - 64 q^{36} + 24 q^{37} - 16 q^{38} + 48 q^{39} - 8 q^{40} - 64 q^{41} + 64 q^{42} - 32 q^{43} - 8 q^{45} - 16 q^{46} - 16 q^{47} - 144 q^{48} + 64 q^{50} - 16 q^{51} - 16 q^{52} - 72 q^{53} + 32 q^{55} - 32 q^{56} - 32 q^{57} - 8 q^{58} + 16 q^{59} + 120 q^{60} - 16 q^{61} - 128 q^{62} - 88 q^{63} + 32 q^{65} - 16 q^{66} + 16 q^{68} - 144 q^{70} - 32 q^{71} - 48 q^{73} + 104 q^{75} - 64 q^{76} + 64 q^{77} + 288 q^{78} - 64 q^{79} - 344 q^{80} + 32 q^{81} - 8 q^{82} - 96 q^{83} + 96 q^{84} + 48 q^{85} - 32 q^{86} - 56 q^{87} + 32 q^{88} - 80 q^{90} - 32 q^{91} + 192 q^{92} - 160 q^{93} + 64 q^{94} - 40 q^{95} + 80 q^{96} - 224 q^{97} - 256 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(595, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
595.2.cm.a 595.cm 595.bm $1088$ $4.751$ None 595.2.cm.a \(-8\) \(-8\) \(-8\) \(-16\) $\mathrm{SU}(2)[C_{48}]$