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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
195.2.bb.a 195.bb 13.e $4$ $1.557$ \(\Q(\zeta_{12})\) None \(-6\) \(-2\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
195.2.bb.b 195.bb 13.e $8$ $1.557$ 8.0.191102976.5 None \(0\) \(4\) \(0\) \(12\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2\beta _{1}+\beta _{3}-\beta _{5}-\beta _{7})q^{2}+(1-\beta _{4}+\cdots)q^{3}+\cdots\)
195.2.bb.c 195.bb 13.e $8$ $1.557$ 8.0.56070144.2 None \(6\) \(-4\) \(0\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{1}-\beta _{2}-\beta _{4}+\beta _{5}+\beta _{6})q^{2}+\cdots\)

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

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