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

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

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

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