Properties

Label 12.17.d
Level $12$
Weight $17$
Character orbit 12.d
Rep. character $\chi_{12}(7,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $1$
Sturm bound $34$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 17 \)
Character orbit: \([\chi]\) \(=\) 12.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(34\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{17}(12, [\chi])\).

Total New Old
Modular forms 34 16 18
Cusp forms 30 16 14
Eisenstein series 4 0 4

Trace form

\( 16 q - 186 q^{2} + 136588 q^{4} + 354144 q^{5} + 1561518 q^{6} + 14683680 q^{8} - 229582512 q^{9} + O(q^{10}) \) \( 16 q - 186 q^{2} + 136588 q^{4} + 354144 q^{5} + 1561518 q^{6} + 14683680 q^{8} - 229582512 q^{9} - 49800172 q^{10} + 425284020 q^{12} - 906419296 q^{13} - 806064072 q^{14} - 2108540816 q^{16} + 12240765600 q^{17} + 2668896702 q^{18} + 1002788712 q^{20} + 39806479296 q^{21} + 216706355928 q^{22} - 111931394832 q^{24} + 206381182512 q^{25} + 1054507182588 q^{26} - 1526063922288 q^{28} + 327679573728 q^{29} + 1192344308100 q^{30} - 5158730488416 q^{32} + 679591529280 q^{33} + 9473293385948 q^{34} - 1959888509316 q^{36} - 8149494749152 q^{37} + 23318999782920 q^{38} - 28671795971776 q^{40} - 25536724613472 q^{41} + 5103781482168 q^{42} - 11442227373552 q^{44} - 5081579320608 q^{45} + 9929654732736 q^{46} + 29246734238832 q^{48} - 93287012964080 q^{49} - 133601044957998 q^{50} + 302261844234872 q^{52} - 86928436629792 q^{53} - 22406076560826 q^{54} + 530930989929024 q^{56} + 48687411524544 q^{57} - 189801665049916 q^{58} + 268455359263896 q^{60} + 476028596468000 q^{61} - 419080420491096 q^{62} + 305944925720704 q^{64} - 1276571708976192 q^{65} - 64815073701480 q^{66} - 1393626893610696 q^{68} + 384812600884992 q^{69} + 1815049064679696 q^{70} - 210694758737760 q^{72} - 368686901901280 q^{73} + 875633111941836 q^{74} - 4351002030861264 q^{76} - 81504772370688 q^{77} + 1907392409236620 q^{78} - 8190389938127328 q^{80} + 3294258113514384 q^{81} + 2390391408733340 q^{82} - 510964995024720 q^{84} + 10085047677398464 q^{85} - 894939801424296 q^{86} + 669091386916800 q^{88} - 5711067674201568 q^{89} + 714578036612004 q^{90} + 7708247605922304 q^{92} + 7132614781502016 q^{93} - 9487273535547696 q^{94} + 8786531038601952 q^{96} - 13564951560560608 q^{97} - 33011660914531290 q^{98} + O(q^{100}) \)

Decomposition of \(S_{17}^{\mathrm{new}}(12, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
12.17.d.a 12.d 4.b $16$ $19.479$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-186\) \(0\) \(354144\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-12-\beta _{1})q^{2}+(\beta _{1}-\beta _{3})q^{3}+(8542+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{17}^{\mathrm{old}}(12, [\chi])\) into lower level spaces

\( S_{17}^{\mathrm{old}}(12, [\chi]) \cong \) \(S_{17}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 2}\)