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Properties

Label 325.2.be
Level $325$
Weight $2$
Character orbit 325.be
Rep. character $\chi_{325}(47,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $264$
Newform subspaces $2$
Sturm bound $70$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 325.be (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 325 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 2 \)
Sturm bound: \(70\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(325, [\chi])\).

Total New Old
Modular forms 296 296 0
Cusp forms 264 264 0
Eisenstein series 32 32 0

Trace form

\( 264 q - 10 q^{2} - 16 q^{3} + 62 q^{4} - 4 q^{5} - 6 q^{6} - 16 q^{7} - 10 q^{8} - 20 q^{9} + O(q^{10}) \) \( 264 q - 10 q^{2} - 16 q^{3} + 62 q^{4} - 4 q^{5} - 6 q^{6} - 16 q^{7} - 10 q^{8} - 20 q^{9} - 8 q^{10} - 6 q^{11} - 20 q^{13} - 20 q^{14} + 34 q^{15} - 66 q^{16} - 14 q^{17} + 12 q^{18} + 10 q^{19} + 46 q^{20} - 36 q^{21} - 28 q^{22} + 20 q^{23} - 20 q^{24} + 6 q^{25} - 16 q^{26} - 40 q^{27} - 38 q^{28} - 40 q^{29} + 16 q^{30} - 6 q^{31} - 40 q^{33} - 58 q^{34} - 4 q^{35} - 40 q^{36} - 36 q^{37} - 8 q^{38} - 50 q^{39} - 48 q^{40} + 14 q^{41} - 40 q^{42} + 4 q^{43} - 18 q^{44} + 26 q^{45} - 6 q^{46} + 12 q^{47} - 4 q^{48} + 168 q^{49} + 44 q^{50} + 42 q^{52} - 6 q^{53} + 94 q^{54} - 36 q^{55} - 140 q^{56} + 86 q^{58} - 10 q^{59} + 6 q^{60} - 12 q^{61} + 40 q^{62} + 10 q^{63} + 62 q^{64} + 108 q^{65} - 12 q^{66} - 10 q^{67} - 22 q^{68} - 88 q^{70} - 6 q^{71} + 2 q^{72} - 90 q^{73} + 96 q^{75} - 120 q^{77} - 74 q^{78} - 20 q^{79} - 178 q^{80} + 22 q^{81} - 74 q^{82} - 140 q^{83} - 48 q^{84} + 72 q^{85} - 26 q^{86} - 36 q^{87} + 16 q^{88} - 20 q^{89} - 90 q^{90} - 136 q^{91} - 64 q^{92} + 140 q^{94} + 48 q^{95} + 124 q^{96} - 10 q^{97} + 120 q^{98} - 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(325, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
325.2.be.a 325.be 325.ae $8$ $2.595$ \(\Q(\zeta_{20})\) None \(0\) \(0\) \(-10\) \(-4\) $\mathrm{SU}(2)[C_{20}]$ \(q+(-\zeta_{20}-\zeta_{20}^{5})q^{2}+(\zeta_{20}+\zeta_{20}^{3}+\cdots)q^{3}+\cdots\)
325.2.be.b 325.be 325.ae $256$ $2.595$ None \(-10\) \(-16\) \(6\) \(-12\) $\mathrm{SU}(2)[C_{20}]$