Properties

Label 195.2.b
Level $195$
Weight $2$
Character orbit 195.b
Rep. character $\chi_{195}(181,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $3$
Sturm bound $56$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 195 = 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 195.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(56\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(195, [\chi])\).

Total New Old
Modular forms 32 8 24
Cusp forms 24 8 16
Eisenstein series 8 0 8

Trace form

\( 8q + 4q^{3} - 4q^{4} + 8q^{9} + O(q^{10}) \) \( 8q + 4q^{3} - 4q^{4} + 8q^{9} - 4q^{10} - 12q^{12} + 4q^{13} - 16q^{14} + 12q^{16} + 24q^{22} - 8q^{23} - 8q^{25} - 16q^{26} + 4q^{27} - 8q^{29} - 4q^{30} - 8q^{35} - 4q^{36} + 24q^{38} - 4q^{39} + 12q^{40} - 16q^{42} - 16q^{43} - 4q^{48} + 4q^{49} - 12q^{51} + 4q^{52} - 16q^{53} + 20q^{55} + 56q^{56} - 20q^{61} - 8q^{62} - 12q^{64} - 8q^{65} + 24q^{66} + 24q^{68} + 4q^{69} + 40q^{74} - 4q^{75} + 56q^{77} - 16q^{78} - 28q^{79} + 8q^{81} + 16q^{82} + 16q^{87} - 80q^{88} - 4q^{90} - 52q^{91} - 80q^{92} - 16q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(195, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
195.2.b.a \(2\) \(1.557\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}+2q^{4}+iq^{5}+3iq^{7}+q^{9}+\cdots\)
195.2.b.b \(2\) \(1.557\) \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) \(q+iq^{2}+q^{3}+q^{4}+iq^{5}+iq^{6}-2iq^{7}+\cdots\)
195.2.b.c \(4\) \(1.557\) \(\Q(i, \sqrt{17})\) None \(0\) \(4\) \(0\) \(0\) \(q+\beta _{1}q^{2}+q^{3}+(-3+\beta _{3})q^{4}-\beta _{2}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(195, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(195, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)