Properties

Label 325.2.o
Level $325$
Weight $2$
Character orbit 325.o
Rep. character $\chi_{325}(74,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $36$
Newform subspaces $3$
Sturm bound $70$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 325.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(70\)
Trace bound: \(4\)
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 44 40
Cusp forms 60 36 24
Eisenstein series 24 8 16

Trace form

\( 36q + 16q^{4} + 6q^{6} + 8q^{9} + O(q^{10}) \) \( 36q + 16q^{4} + 6q^{6} + 8q^{9} - 6q^{11} + 40q^{14} + 4q^{16} - 8q^{19} - 20q^{24} - 30q^{26} - 10q^{29} - 32q^{31} - 84q^{34} + 42q^{36} + 20q^{39} - 36q^{41} - 8q^{44} - 14q^{46} - 2q^{49} - 48q^{51} + 58q^{54} + 2q^{56} - 10q^{61} + 20q^{64} + 68q^{66} + 8q^{69} + 2q^{71} - 16q^{74} + 4q^{76} + 72q^{79} - 18q^{81} - 104q^{84} - 48q^{86} - 52q^{89} - 6q^{91} - 70q^{94} + 76q^{96} - 176q^{99} + O(q^{100}) \)

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.o.a \(8\) \(2.595\) 8.0.12960000.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}+(\beta _{3}+2\beta _{6}+\beta _{7})q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots\)
325.2.o.b \(8\) \(2.595\) 8.0.592240896.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(1-2\beta _{3}+\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
325.2.o.c \(20\) \(2.595\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{10}q^{3}+(\beta _{7}+\beta _{11})q^{4}+\cdots\)

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

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