Properties

Label 195.2.bb
Level $195$
Weight $2$
Character orbit 195.bb
Rep. character $\chi_{195}(121,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $3$
Sturm bound $56$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 195 = 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 195.bb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(56\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 64 20 44
Cusp forms 48 20 28
Eisenstein series 16 0 16

Trace form

\( 20q - 2q^{3} + 12q^{4} + 6q^{7} - 10q^{9} + O(q^{10}) \) \( 20q - 2q^{3} + 12q^{4} + 6q^{7} - 10q^{9} + 4q^{10} - 8q^{12} - 2q^{13} - 8q^{14} - 8q^{16} - 12q^{17} - 12q^{19} - 24q^{20} + 12q^{22} - 4q^{23} - 20q^{25} - 32q^{26} + 4q^{27} - 12q^{28} + 8q^{29} + 4q^{30} + 60q^{32} - 4q^{35} + 12q^{36} - 12q^{37} - 4q^{39} + 24q^{40} - 20q^{42} + 18q^{43} + 72q^{46} - 24q^{48} + 24q^{51} + 36q^{52} - 32q^{53} - 8q^{55} + 16q^{56} - 24q^{58} + 30q^{61} - 52q^{62} - 6q^{63} - 16q^{64} + 20q^{65} - 24q^{66} - 30q^{67} + 24q^{68} - 4q^{69} + 48q^{71} - 4q^{74} + 2q^{75} - 48q^{76} + 40q^{77} - 8q^{78} + 20q^{79} - 10q^{81} - 16q^{82} + 36q^{84} - 16q^{87} + 8q^{88} + 24q^{89} - 8q^{90} - 26q^{91} + 8q^{92} - 6q^{93} + 24q^{94} - 8q^{95} - 18q^{97} - 96q^{98} + O(q^{100}) \)

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.bb.a \(4\) \(1.557\) \(\Q(\zeta_{12})\) None \(-6\) \(-2\) \(0\) \(-12\) \(q+(-1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
195.2.bb.b \(8\) \(1.557\) 8.0.191102976.5 None \(0\) \(4\) \(0\) \(12\) \(q+(2\beta _{1}+\beta _{3}-\beta _{5}-\beta _{7})q^{2}+(1-\beta _{4}+\cdots)q^{3}+\cdots\)
195.2.bb.c \(8\) \(1.557\) 8.0.56070144.2 None \(6\) \(-4\) \(0\) \(6\) \(q+(1-\beta _{1}-\beta _{2}-\beta _{4}+\beta _{5}+\beta _{6})q^{2}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(195, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)