Properties

Label 325.2.c
Level $325$
Weight $2$
Character orbit 325.c
Rep. character $\chi_{325}(51,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $7$
Sturm bound $70$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 325.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(70\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(2\), \(3\), \(7\)

Dimensions

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

Total New Old
Modular forms 42 24 18
Cusp forms 30 18 12
Eisenstein series 12 6 6

Trace form

\( 18 q + 4 q^{3} - 10 q^{4} + 6 q^{9} + O(q^{10}) \) \( 18 q + 4 q^{3} - 10 q^{4} + 6 q^{9} + 8 q^{13} + 12 q^{14} - 14 q^{16} - 8 q^{17} + 24 q^{22} - 16 q^{23} - 6 q^{26} + 28 q^{27} - 12 q^{29} - 10 q^{36} + 20 q^{38} + 4 q^{39} - 44 q^{42} - 24 q^{43} - 36 q^{48} - 30 q^{49} - 24 q^{51} - 20 q^{52} - 12 q^{53} + 12 q^{56} + 44 q^{61} - 8 q^{62} + 6 q^{64} + 16 q^{66} + 88 q^{68} - 12 q^{69} + 12 q^{74} - 36 q^{77} + 52 q^{78} + 44 q^{79} - 54 q^{81} + 28 q^{82} + 4 q^{87} - 60 q^{88} - 24 q^{91} + 20 q^{92} + 52 q^{94} + O(q^{100}) \)

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.c.a $2$ $2.595$ \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(0\) \(0\) \(q+iq^{2}-2q^{3}+q^{4}-2iq^{6}-5iq^{7}+\cdots\)
325.2.c.b $2$ $2.595$ \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(0\) \(0\) \(q+iq^{2}-2q^{3}+q^{4}-2iq^{6}+3iq^{8}+\cdots\)
325.2.c.c $2$ $2.595$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+iq^{2}-q^{3}-2q^{4}-iq^{6}+iq^{7}+\cdots\)
325.2.c.d $2$ $2.595$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) \(q+iq^{2}+q^{3}-2q^{4}+iq^{6}+iq^{7}+\cdots\)
325.2.c.e $2$ $2.595$ \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(0\) \(0\) \(q+iq^{2}+2q^{3}+q^{4}+2iq^{6}+3iq^{8}+\cdots\)
325.2.c.f $2$ $2.595$ \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(0\) \(0\) \(q+iq^{2}+2q^{3}+q^{4}+2iq^{6}-5iq^{7}+\cdots\)
325.2.c.g $6$ $2.595$ 6.0.5089536.1 None \(0\) \(4\) \(0\) \(0\) \(q-\beta _{4}q^{2}+(1+\beta _{1})q^{3}+(-2+\beta _{3})q^{4}+\cdots\)

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

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