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Properties

Label 130.6.b
Level $130$
Weight $6$
Character orbit 130.b
Rep. character $\chi_{130}(79,\cdot)$
Character field $\Q$
Dimension $30$
Newform subspaces $2$
Sturm bound $126$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 130 = 2 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 130.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(126\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(130, [\chi])\).

Total New Old
Modular forms 110 30 80
Cusp forms 102 30 72
Eisenstein series 8 0 8

Trace form

\( 30 q - 480 q^{4} - 160 q^{5} + 224 q^{6} - 3058 q^{9} + O(q^{10}) \) \( 30 q - 480 q^{4} - 160 q^{5} + 224 q^{6} - 3058 q^{9} + 496 q^{10} - 148 q^{11} - 80 q^{14} + 864 q^{15} + 7680 q^{16} - 1444 q^{19} + 2560 q^{20} - 11528 q^{21} - 3584 q^{24} - 7016 q^{25} + 4056 q^{26} + 7732 q^{29} + 10056 q^{30} - 6088 q^{31} - 9248 q^{34} - 1566 q^{35} + 48928 q^{36} - 7936 q^{40} + 23636 q^{41} + 2368 q^{44} + 77188 q^{45} - 28976 q^{46} - 29538 q^{49} - 1216 q^{50} - 90948 q^{51} - 13856 q^{54} - 56720 q^{55} + 1280 q^{56} - 153156 q^{59} - 13824 q^{60} + 167540 q^{61} - 122880 q^{64} - 676 q^{65} - 101568 q^{66} + 279432 q^{69} - 191888 q^{70} - 57040 q^{71} + 7680 q^{74} + 55550 q^{75} + 23104 q^{76} + 109928 q^{79} - 40960 q^{80} + 519526 q^{81} + 184448 q^{84} + 4428 q^{85} + 238400 q^{86} - 491148 q^{89} + 2808 q^{90} + 107484 q^{91} - 96400 q^{94} + 716 q^{95} + 57344 q^{96} - 449236 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(130, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
130.6.b.a 130.b 5.b $12$ $20.850$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 130.6.b.a \(0\) \(0\) \(-80\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-4\beta _{5}q^{2}+(2\beta _{5}+\beta _{8})q^{3}-2^{4}q^{4}+\cdots\)
130.6.b.b 130.b 5.b $18$ $20.850$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None 130.6.b.b \(0\) \(0\) \(-80\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-4\beta _{4}q^{2}+(\beta _{1}+2\beta _{4})q^{3}-2^{4}q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(130, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(130, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)