↑

Properties

Label 603.2.h
Level $603$
Weight $2$
Character orbit 603.h
Rep. character $\chi_{603}(364,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $132$
Newform subspaces $3$
Sturm bound $136$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 603 = 3^{2} \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 603.h (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 603 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
Sturm bound: \(136\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(603, [\chi])\).

Total New Old
Modular forms 140 140 0
Cusp forms 132 132 0
Eisenstein series 8 8 0

Trace form

\( 132 q - 6 q^{2} - 3 q^{3} + 126 q^{4} + 3 q^{5} - 6 q^{6} - 24 q^{8} - 7 q^{9} + O(q^{10}) \) \( 132 q - 6 q^{2} - 3 q^{3} + 126 q^{4} + 3 q^{5} - 6 q^{6} - 24 q^{8} - 7 q^{9} + 7 q^{11} - 7 q^{12} - 4 q^{14} + 114 q^{16} + q^{17} - 4 q^{18} + 5 q^{20} - 9 q^{21} - 12 q^{22} + 5 q^{23} - 39 q^{24} - 57 q^{25} + 2 q^{26} - 24 q^{27} - 12 q^{28} + 7 q^{29} - 16 q^{30} - 74 q^{32} - 3 q^{33} + 3 q^{35} - 12 q^{36} + 10 q^{38} - 19 q^{39} - 12 q^{40} - 10 q^{41} + 24 q^{42} - 3 q^{43} - 10 q^{44} + 9 q^{45} + 16 q^{47} - 28 q^{48} - 48 q^{49} - 22 q^{50} + 12 q^{51} - 12 q^{52} - 36 q^{53} - 15 q^{54} + 6 q^{55} + 2 q^{56} + 17 q^{57} - 6 q^{58} + 6 q^{59} + 35 q^{60} + 36 q^{61} - 54 q^{62} + 29 q^{63} + 84 q^{64} + 24 q^{65} + 48 q^{66} + 9 q^{67} - 21 q^{68} - 40 q^{69} + 33 q^{70} + 4 q^{71} - 25 q^{72} + 23 q^{74} - 20 q^{75} + 3 q^{76} + 21 q^{77} - 18 q^{78} + 3 q^{79} + 16 q^{80} - 27 q^{81} - 26 q^{83} - 35 q^{84} + 6 q^{85} - 8 q^{86} - 52 q^{87} - 21 q^{88} + 124 q^{89} - 109 q^{90} - 42 q^{91} + 8 q^{92} - q^{93} + 70 q^{95} - 17 q^{96} - 30 q^{97} - 53 q^{98} + 70 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(603, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
603.2.h.a 603.h 603.h $2$ $4.815$ \(\Q(\sqrt{-3}) \) None 603.2.f.a \(-2\) \(0\) \(-3\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(-1+2\zeta_{6})q^{3}-q^{4}+(-3+\cdots)q^{5}+\cdots\)
603.2.h.b 603.h 603.h $2$ $4.815$ \(\Q(\sqrt{-3}) \) None 603.2.f.b \(-2\) \(0\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(1-2\zeta_{6})q^{3}-q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
603.2.h.c 603.h 603.h $128$ $4.815$ None 603.2.f.c \(-2\) \(-3\) \(5\) \(4\) $\mathrm{SU}(2)[C_{3}]$