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Properties

Label 12.15.d
Level $12$
Weight $15$
Character orbit 12.d
Rep. character $\chi_{12}(7,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $1$
Sturm bound $30$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 15 \)
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: \(30\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{15}(12, [\chi])\).

Total New Old
Modular forms 30 14 16
Cusp forms 26 14 12
Eisenstein series 4 0 4

Trace form

\( 14 q + 182 q^{2} + 9308 q^{4} - 16124 q^{5} + 56862 q^{6} + 4352816 q^{8} - 22320522 q^{9} + O(q^{10}) \) \( 14 q + 182 q^{2} + 9308 q^{4} - 16124 q^{5} + 56862 q^{6} + 4352816 q^{8} - 22320522 q^{9} + 586324 q^{10} + 621108 q^{12} + 109934140 q^{13} - 200755992 q^{14} + 380631536 q^{16} - 291483380 q^{17} - 290166786 q^{18} + 5316726088 q^{20} - 1117661976 q^{21} - 9373833288 q^{22} + 2880331488 q^{24} + 12506859258 q^{25} - 45510637748 q^{26} + 83579713776 q^{28} - 12126204812 q^{29} - 44941179132 q^{30} + 67974212192 q^{32} - 34345330344 q^{33} - 57269346212 q^{34} - 14839958484 q^{36} + 119365701580 q^{37} + 102957884712 q^{38} - 491601579872 q^{40} + 189318893932 q^{41} + 240539889384 q^{42} - 997611383472 q^{44} + 25706864052 q^{45} + 1368039641184 q^{46} - 465649986384 q^{48} - 769149171250 q^{49} + 2170057449522 q^{50} - 2399333559176 q^{52} + 1251391890964 q^{53} - 90656394426 q^{54} + 2319191796096 q^{56} + 1805052294792 q^{57} - 5157502168892 q^{58} + 2354207329944 q^{60} - 7882441676660 q^{61} - 9161379391272 q^{62} + 17520900128384 q^{64} + 5858206778312 q^{65} - 6614704234440 q^{66} + 18747786717976 q^{68} - 13777261381728 q^{69} - 8213486211792 q^{70} - 6939794663568 q^{72} + 39185062250428 q^{73} - 7698562888484 q^{74} - 9224963770896 q^{76} - 41289727781472 q^{77} + 10470873014172 q^{78} - 57127847610848 q^{80} + 35586121596606 q^{81} + 107070799921084 q^{82} - 28102976768880 q^{84} - 188880254078680 q^{85} + 102443851819896 q^{86} - 83262676567680 q^{88} + 223721333984572 q^{89} - 934789838652 q^{90} - 79895035003584 q^{92} + 12688158423960 q^{93} - 52692266305296 q^{94} - 2264434006752 q^{96} + 282902280361756 q^{97} - 228639957171082 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{15}^{\mathrm{new}}(12, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
12.15.d.a 12.d 4.b $14$ $14.919$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(182\) \(0\) \(-16124\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(13-\beta _{1})q^{2}+\beta _{2}q^{3}+(665-13\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{15}^{\mathrm{old}}(12, [\chi])\) into lower level spaces

\( S_{15}^{\mathrm{old}}(12, [\chi]) \cong \) \(S_{15}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 2}\)