Properties

Label 325.2.m
Level $325$
Weight $2$
Character orbit 325.m
Rep. character $\chi_{325}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $40$
Newform subspaces $4$
Sturm bound $70$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 325.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(70\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 80 48 32
Cusp forms 56 40 16
Eisenstein series 24 8 16

Trace form

\( 40q - 18q^{4} - 6q^{6} + 26q^{9} + O(q^{10}) \) \( 40q - 18q^{4} - 6q^{6} + 26q^{9} - 18q^{11} + 8q^{14} - 18q^{16} - 12q^{19} - 48q^{24} - 8q^{26} + 8q^{29} + 36q^{36} - 44q^{39} + 30q^{41} - 42q^{46} - 8q^{49} - 8q^{51} - 42q^{54} - 18q^{56} + 96q^{59} - 32q^{61} + 88q^{64} - 60q^{66} - 32q^{69} - 42q^{71} + 62q^{74} + 72q^{76} + 8q^{79} + 4q^{81} + 240q^{84} - 72q^{89} + 82q^{91} - 62q^{94} + O(q^{100}) \)

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.m.a \(4\) \(2.595\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{2}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots\)
325.2.m.b \(8\) \(2.595\) 8.0.22581504.2 None \(-2\) \(6\) \(0\) \(10\) \(q+(1-\beta _{1}-\beta _{3}-\beta _{6})q^{2}+(2-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
325.2.m.c \(8\) \(2.595\) 8.0.22581504.2 None \(2\) \(-6\) \(0\) \(-10\) \(q+(-1+\beta _{1}+\beta _{3}+\beta _{6})q^{2}+(-2+\beta _{3}+\cdots)q^{3}+\cdots\)
325.2.m.d \(20\) \(2.595\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{12}q^{2}+(-\beta _{13}+\beta _{17}-\beta _{19})q^{3}+\cdots\)

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

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