Properties

Label 325.2.b
Level $325$
Weight $2$
Character orbit 325.b
Rep. character $\chi_{325}(274,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $6$
Sturm bound $70$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 325.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(70\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

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

Total New Old
Modular forms 42 18 24
Cusp forms 30 18 12
Eisenstein series 12 0 12

Trace form

\( 18 q - 10 q^{4} - 12 q^{6} - 14 q^{9} + O(q^{10}) \) \( 18 q - 10 q^{4} - 12 q^{6} - 14 q^{9} + 12 q^{11} - 4 q^{14} + 2 q^{16} + 8 q^{19} - 12 q^{21} + 8 q^{24} + 6 q^{26} + 28 q^{29} + 8 q^{31} + 18 q^{36} - 8 q^{39} - 76 q^{44} - 28 q^{46} - 22 q^{49} + 92 q^{54} - 44 q^{56} - 48 q^{59} - 44 q^{61} + 70 q^{64} - 8 q^{66} + 28 q^{69} + 52 q^{71} + 4 q^{74} - 40 q^{76} - 12 q^{79} - 30 q^{81} + 80 q^{84} + 84 q^{86} + 16 q^{89} + 4 q^{94} + 32 q^{96} - 76 q^{99} + O(q^{100}) \)

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.b.a $2$ $2.595$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{2}-iq^{3}-2q^{4}+2q^{6}+2iq^{7}+\cdots\)
325.2.b.b $2$ $2.595$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-2iq^{3}+q^{4}+2q^{6}+4iq^{7}+\cdots\)
325.2.b.c $2$ $2.595$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+2q^{4}+4iq^{7}+2q^{9}-6q^{11}+\cdots\)
325.2.b.d $4$ $2.595$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+2\zeta_{8}^{2}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
325.2.b.e $4$ $2.595$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}+(-\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots\)
325.2.b.f $4$ $2.595$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}-\zeta_{8}^{2}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)

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

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