Properties

Label 325.2.e
Level $325$
Weight $2$
Character orbit 325.e
Rep. character $\chi_{325}(126,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $40$
Newform subspaces $5$
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.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 5 \)
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 80 52 28
Cusp forms 56 40 16
Eisenstein series 24 12 12

Trace form

\( 40 q + 2 q^{3} - 18 q^{4} - 10 q^{6} + 2 q^{7} + 12 q^{8} - 14 q^{9} + O(q^{10}) \) \( 40 q + 2 q^{3} - 18 q^{4} - 10 q^{6} + 2 q^{7} + 12 q^{8} - 14 q^{9} - 6 q^{11} + 4 q^{12} + 4 q^{13} + 8 q^{14} - 18 q^{16} + 10 q^{17} - 8 q^{18} - 4 q^{19} - 24 q^{21} - 4 q^{22} + 6 q^{23} - 8 q^{24} + 20 q^{27} - 10 q^{28} - 12 q^{29} - 32 q^{31} - 2 q^{32} - 14 q^{33} + 80 q^{34} + 32 q^{36} + 6 q^{37} - 24 q^{38} + 12 q^{39} - 10 q^{41} - 4 q^{42} - 14 q^{43} - 8 q^{44} + 10 q^{46} - 24 q^{47} + 12 q^{48} - 12 q^{49} - 18 q^{52} - 40 q^{53} - 26 q^{54} + 2 q^{56} - 12 q^{57} + 32 q^{58} + 16 q^{59} - 4 q^{61} + 4 q^{62} + 12 q^{63} - 8 q^{64} + 124 q^{66} - 6 q^{67} + 34 q^{68} - 30 q^{71} + 12 q^{72} + 56 q^{73} - 2 q^{74} - 32 q^{76} - 4 q^{77} - 12 q^{78} + 40 q^{79} - 24 q^{81} - 20 q^{82} + 8 q^{83} - 4 q^{84} - 112 q^{86} - 18 q^{87} + 2 q^{88} + 16 q^{89} - 30 q^{91} + 20 q^{92} - 8 q^{93} + 10 q^{94} + 84 q^{96} - 22 q^{97} - 12 q^{98} + 40 q^{99} + O(q^{100}) \)

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.e.a \(4\) \(2.595\) \(\Q(\sqrt{-3}, \sqrt{13})\) None \(-1\) \(2\) \(0\) \(-2\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{3}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
325.2.e.b \(4\) \(2.595\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(1\) \(0\) \(0\) \(4\) \(q+\beta _{1}q^{2}+(1-2\beta _{1}+\beta _{3})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
325.2.e.c \(10\) \(2.595\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(-3\) \(0\) \(2\) \(q+\beta _{1}q^{2}+(-1-\beta _{4}+\beta _{6}+\beta _{8})q^{3}+\cdots\)
325.2.e.d \(10\) \(2.595\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(3\) \(0\) \(-2\) \(q-\beta _{1}q^{2}+(1+\beta _{4}-\beta _{6}-\beta _{8})q^{3}+(-\beta _{6}+\cdots)q^{4}+\cdots\)
325.2.e.e \(12\) \(2.595\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}+(\beta _{6}-\beta _{11})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)

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

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