Properties

Label 325.2.n
Level $325$
Weight $2$
Character orbit 325.n
Rep. character $\chi_{325}(101,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $38$
Newform subspaces $6$
Sturm bound $70$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 325.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(70\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 84 50 34
Cusp forms 60 38 22
Eisenstein series 24 12 12

Trace form

\( 38 q + 3 q^{2} + 17 q^{4} + 6 q^{7} - 13 q^{9} + O(q^{10}) \) \( 38 q + 3 q^{2} + 17 q^{4} + 6 q^{7} - 13 q^{9} - 18 q^{11} - 16 q^{12} + 5 q^{13} - 24 q^{14} - 23 q^{16} - q^{17} + 18 q^{19} + 12 q^{22} + 4 q^{23} + 54 q^{24} - 39 q^{26} + 12 q^{27} + 18 q^{28} + 3 q^{29} + 3 q^{32} - 42 q^{33} + 11 q^{36} - 21 q^{37} + 4 q^{38} + 10 q^{39} + 27 q^{41} - 4 q^{42} + 10 q^{43} + 60 q^{46} - 38 q^{48} - 13 q^{49} + 12 q^{51} + 4 q^{52} + 30 q^{53} - 18 q^{54} - 42 q^{56} - 45 q^{58} - 36 q^{59} + 21 q^{61} - 10 q^{62} + 24 q^{63} - 14 q^{64} - 100 q^{66} - 12 q^{67} + 17 q^{68} + 36 q^{69} - 36 q^{71} + 45 q^{72} - 15 q^{74} + 30 q^{76} + 36 q^{77} + 80 q^{78} - 48 q^{79} - 19 q^{81} - 13 q^{82} - 204 q^{84} - 16 q^{87} + 18 q^{88} + 12 q^{89} + 42 q^{91} - 56 q^{92} + 12 q^{93} - 4 q^{94} + 18 q^{97} - 93 q^{98} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
325.2.n.a $2$ $2.595$ \(\Q(\sqrt{-3}) \) None \(3\) \(2\) \(0\) \(0\) \(q+(1+\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
325.2.n.b $4$ $2.595$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(-3\) \(2\) \(0\) \(6\) \(q+(-1+\beta _{3})q^{2}+\beta _{2}q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
325.2.n.c $4$ $2.595$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(3\) \(-2\) \(0\) \(-6\) \(q+(1-\beta _{3})q^{2}-\beta _{2}q^{3}+(\beta _{1}+\beta _{2}-2\beta _{3})q^{4}+\cdots\)
325.2.n.d $8$ $2.595$ 8.0.22581504.2 None \(0\) \(-2\) \(0\) \(6\) \(q+(\beta _{3}+\beta _{5}+\beta _{7})q^{2}+(-1+\beta _{1}+2\beta _{2}+\cdots)q^{3}+\cdots\)
325.2.n.e $10$ $2.595$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(-3\) \(0\) \(-6\) \(q-\beta _{3}q^{2}+(-1-\beta _{2}-\beta _{8}+\beta _{9})q^{3}+\cdots\)
325.2.n.f $10$ $2.595$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(3\) \(0\) \(6\) \(q+(\beta _{1}+\beta _{3})q^{2}+(-\beta _{2}+\beta _{9})q^{3}+(2+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(325, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(325, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)